text:
\section*{Nomenclature}
\noindent\begin{tabular}{@{}lcp{4.5in}@{}}
$\beta$,$\gamma (\in \mathbb{S}^1) $ &=&
The gimbal and wheel angles. (\(rad\))\\
$R_{\beta} (\in \mathop{\mathbb{SO}(3)})$ &=&
Transformation from gimbal frame $\mathcal{G}$
to the spacecraft body frame $\mathcal{B}$.\\
$\mathbb{I}_{s}$ &=&
Spacecraft inertia without the CMG gimbal and wheel inertia. (\(kg.m^2\))\\
$I_{g},\,I_{r}$ &=&
Gimbal frame inertia, wheel inertia about own centre of mass represented in gimbal frame. (\(kg.m^2\))\\
$(\mathbb{I}_{gr})_{\beta}$ &=&
Combined inertia of gimbal frame and wheel in the spacecraft frame.
$R_{\beta}  \mathbb{I}_{gr} R_{\beta}^T$. (\(kg.m^2\))\\
$\tilde{I}_{(\beta)}$ &=&
Locked inertia tensor.\\
$X$ &=&
State variable
$\triangleq(R_{s},\beta,\gamma)\triangleq(R_{s},x)$.\\
$\Omega_{s}$ &=&
Angular velocity of the spacecraft in the  body frame. (\(rad/s\))\\
$\mu$ &=&
Total spatial angular momentum of the spacecraft in inertial frame. (\(kg.m^2/s\))\\
$i_{2},i_{3}$ &=&
The vectors
$[0\,1\,0]^{T}$ and
$[0\,0\,1]^{T}$.\\
$\mathcal{S}(\ ),\widehat{(\ )}$ &=&
Mapping
$\mathbb{R}^{3}\rightarrow\mathfrak{so}(3)$
such that
$\mathcal{S}(\vec{a})\vec{b}\triangleq\hat{\vec{a}}\cdot\vec{b}\triangleq\vec{a}\times\vec{b}$.
\end{tabular} \\

\section{Introduction}
Spacecrafts are actuated by two principles - internal or external actuation. The actuators in the former
class consist of momentum wheels (also called internal rotors) and control moment gyros (CMGs).
A refinement of CMGs are the variable speed CMGs (called VSCMGs).
Examples of external actuation systems include gas jet thrusters mounted
on the outer body of the spacecraft.
In this article we focus on spacecraft with gimbals (or the VSCMG)
as the mechanism of actuation.

The modelling of  a spacecraft with a VSCMG has been reported in the literature
\cite{schaub_feedback_1998,schaub_singularity_2000}.
Studies on singularity issues of this system are found in
\cite{tsiotras_singularity_2004,schaub_singularity_2000}. Control
law synthesis and avoidance of singularities are found in
\cite{bedrossian_thesis_1987,margulies_aubrun_1978,
schaub_singularity_2000,tsiotras_singularity_2004} An early
study of singularity in a geometric framework is \cite{kurokawa_geometric_1998}.
That study considers possibility of avoiding singular
gimbal angle configurations using global control.
The analysis proceeds by considering the inverse images of
CMG system angular momenta as union of sub\emph{``manifolds''} of the n-dimensional
gimbal angle configuration space.
The nature of these manifolds are examined at and near singular gimbal configurations.

Spurred by the insight and creativity of J. E. Marsden
\cite{marsden2013introduction} ,the geometric mechanics community
\cite{bloch_nonholo_mech_ctrl,ostrowski1999computing} has studied very
many mechanical systems in the geometric framework. This
framework has proved beneficial
in providing insight into these systems and their structure by preserving the mechanical
objects (momentum, energy) of these systems and also proving useful in
control design \cite{bloch2001controlledlagrangian,bloch2000controlled}.

A geometric description of the VSCMG system based on variational principles is
studied in \cite{sanyal2013vscmg}. The configuration space of the system
is shown to be a principal fiber bundle and the expression for
the Ehressmann connection is derived.
The paper considers a general system where the rotor mass centre is
offset from the gimbal axis.
A stabilising control law is derived as a function of the
internal momentum. Singularity analysis of this system under
typical simplifying assumptions is explored in \cite{sanyal2015vscmg}.
The system is discretised into a model which preserves the conserved
quantities using variational integrators.

While studying the problem of interconnected mechanical systems, the geometry of
the configuration space which is a differential manifold requires attention for
elegant and insightful solutions.
This configuration space $Q$, is often written as the product of two manifolds.
One component is the base manifold $M$, which in our context describes the configuration
of the gimbals mounted
inside the spacecraft. The other
component of the configuration variables depicting the attitude of the spacecraft is
a Lie group $G$, in this case $\mathop{\mathbb{SO}(3)}$
\cite{boothby1975introduction}. The total configuration space of the
spacecraft $Q$ then naturally appears as a product $G \times M$.
Such systems follow the topology of a trivial principal fiber bundle,
see \cite{kobayashi1963foundations}.
Figure \ref{fiber_bundle} shows an explanatory figure of a fiber bundle. The components of
the 2-tuple
$q = (x, g)$ denote the base and the group variable respectively.  The projection map $\pi:
Q \mathop{\rightarrow} M$ maps the configuration space to the base space.
With such a separation of the configuration space, locomotion is readily seen as
the means by which changes in shape affect the macro position.
We refer to \cite{kelly1995geometric,bloch_nonholo_mech_ctrl}
for a detailed explanation on the topology of locomoting systems.

\begin{figure}[h!]
    \centering
    \includegraphics[scale=0.6]{pfb01.png}
    \caption{Fiber Bundle}
    \label{fiber_bundle}
\end{figure}

In this article we present a completely geometric approach to the modelling of the
VSCMG-spacecraft system and relate it to a conventional modelling approach.

\section{Modelling in a geometric framework}
    The configuration space of the spacecraft-gimbal system (with one CMG) is $Q = \mathop{\mathbb{SO}(3)} \times \mathbb{S}^1 \times \mathbb{S}^1 $
    and any arbitrary configuration is expressed by the 3-tuple $(R_s, \beta, \gamma)$, where
    the first element denotes the
    attitude $R_s$ of the spacecraft with respect to fixed / inertial frame, the second denotes the degree of
    freedom $\beta$ of the gimbal frame, the third denotes the degree of freedom
    $\gamma$ of the
    rotor about its  spin axis. For the purpose of later geometrical interpretation, we club
    $x \stackrel{\triangle}{=} (\beta, \gamma)$. There are three rigid bodies involved here,
    each having relative motion (rotation) about the other. Therefore, three frames of reference
    are chosen (apart from the inertial frame) - the first is the
    spacecraft, denoted by the subscript $s$, the second is the gimbal frame, denoted by the
    subscript $g$, the third is the rotor frame, denoted by the subscript $r$.
    The moments of inertia of the homogeneous rotor and the gimbal in their respective
    body frames are assumed to be
    %
    \begin{align}
    \mathbb{I}_{r}=  \pmat{J_x & 0 & 0 \\ 0 & J_x &  0  \\  0  &  0  & J_z } \;\;\;
    \mathbb{I}_{g} = \pmat{I_t & 0 & 0 \\ 0 & I_g &  0  \\  0  &  0  & I_s }
    \end{align}
    Since the rotor is
    assumed to be homogeneous and symmetric, its inertia is represented in the gimbal frame  and
    the combined gimbal-rotor inertia is rewritten as
    %
    \begin{align}
    \mathbb{I}_{gr}= \pmat{(J_x + I_t)& 0 & 0 \\ 0 & (J_x + I_g) &  0  \\  0  &  0  & (J_z + I_s) }
    \end{align}
    %
    If the rotational transformation that relates the gimbal frame to the spacecraft frame is
    given by $R_{\beta}$, where
    $\beta$ denotes the gimballing angle,
    then the gimbal-rotor inertia reflected in the spacecraft frame is
    %
    \begin{align}
    (\mathbb{I}_{gr})_\beta \stackrel{\triangle}{=} R_{\beta}  \mathbb{I}_{gr} R_{\beta}^T
    \end{align}
    %
    Here the subscript $\beta$ denotes the dependance on the gimbal angle $\beta$.
    %
    \subsection{Kinetic energy and a Riemannian structure}
    %
	     The angular velocity of the spacecraft, $\Omega_s \in \mathbb{R}^3$,
	     represented as a skew-symmetric matrix $ {\hat{\Omega}_s} $,
	     is an element of the Lie algebra
    $\mathfrak{so(3)}$. The inner product on this Lie algebra $\mathfrak{so(3)}$
    is defined  in terms of the
    standard inner product on $\mathbb{R}^3$ as
    %
    \begin{align}
    \inprod{\hat{\Omega}_1}{\hat{\Omega}_2}_{\mathfrak{so(3)}}     \stackrel{\triangle}{=}  \frac{1}{2} \inprod{  \Omega_1}{   \mathbb{I}_{s}  \Omega_2}_{\mathbb{R}^3}.
    \end{align}
    %
	     and denotes the kinetic energy of the spacecraft body.
    %
    The kinetic energy of the gimbal-rotor unit is given by
    %
    \begin{align}
    \frac{1}{2} \inprod{R_{\beta}^T \Omega_s + \pmat{0 \\ \dot{\beta} \\ \dot{\gamma}} }
    {\mathbb{I}_{gr}  [ R_{\beta}^T \Omega_s + \pmat{0 \\ \dot{\beta} \\ \dot{\gamma}} ] }
    \end{align}
    %
		and the total kinetic energy of the entire spacecraft-gimbal system is
    %
    \begin{align}
    %
    \frac{1}{2} \inprod{  \pmat{\Omega_s \\ 0 \\ \dot{\beta} \\ \dot{\gamma}}   }
    { \mathbb{I}_{total}   \pmat{\Omega_s \\ 0 \\ \dot{\beta} \\ \dot{\gamma}}     },
    %
    \end{align}
    %
    where
    %
    \begin{align}
    %
    \mathbb{I}_{total}(\beta)= \pmat{ (R_{\beta}  \mathbb{I}_{gr} R_{\beta}^T + \mathbb{I}_{s})  &  R_{\beta} \mathbb{I}_{gr}  \\  \mathbb{I}_{gr}
        R_{\beta}^T &  \mathbb{I}_{gr}   }.
    %
    \end{align}

    It is to be noted that the inertia matrix is dependant on the gimbal angle, $\beta$.
    %

    The kinetic energy induces a metric on the configuration space $Q$ of the
    system, which enables us to impart a {\it Riemannian structure}
    to the system. The Riemannian metric $\mathbb{G}$ defines a smoothly varying
    inner product on
    each tangent space of $Q$.  For $q = (R_s, (\beta, \gamma)) \in Q $ and
    $v_q = (R_s\hat{\Omega}_1, (v_\beta,v_\gamma)),
    w_q = (R_s\hat{\Omega}_2, (w_\beta,w_\gamma)) \in T_qQ$, the Riemannian metric
    is defined as
    %
    \begin{align}
    %
    \inprod{v_q}{w_q}_{\mathbb{G}} & =  \mathbb{G}(q) (v_q, w_q)  \nonumber \\

    & =   \mathbb{G} ( R_s, (\beta, \gamma)) \left( (R_s \hat{\Omega}_1 , (v_\beta, v_\gamma)),
    (R_s \hat{\Omega}_2 , (w_\beta, w_\gamma))\right)
    \end{align}
    %
    \begin{align}
    =  \frac{1}{2} \inprod{  \pmat{R_s \hat{\Omega}_1 \\ 0 \\ v_\beta \\ v_\gamma }   }
    { \mathbb{I}_{total}   \pmat{R_s \hat{\Omega}_2 \\ 0 \\ w_\beta \\  w_\gamma }     }
    %
    \end{align}
    %
    Here $\hat{\Omega}_1$ and
    $ \hat{\Omega}_2$
    belong to the Lie algebra $\mathfrak{so(3)}$. Note that we have used the left-invariant property
    of the vector field on $\mathop{\mathbb{SO}(3)}$, and the fact that the Riemannian metric on $\mathop{\mathbb{SO}(3)}$
    is induced by the inner product on the Lie algebra $\mathfrak{so(3)}$, wherein
    %
    \begin{align}
    \inprod{v_R}{w_R}_{\mathop{\mathbb{SO}(3)}} \stackrel{\triangle}{=} \inprod{\hat{\Omega}_1}{\hat{\Omega}_2}_{\mathfrak{so(3)}} ,
    \end{align}
    %
    where $v_R = R \hat{\Omega}_1$ and $w_R = R \hat{\Omega}_2$, the left translations
    by $R$ of $\hat{\Omega}_1$ and $\hat{\Omega}_2$, respectively.
    %
    \subsection{Group action and a principal fiber bundle}

    The action of the $\mathop{\mathbb{SO}(3)}$ group  on $Q$ induces more geometric structure into
    the 	problem.
    Given $M \in \mathop{\mathbb{SO}(3)}$, the action  is defined by
    %
    \begin{align}
    \mathop{\mathbb{SO}(3)} \times Q \mathop{\rightarrow} Q \;\;\;\;\;\;   (M , (R_s, \beta, \gamma))  \mathop{\rightarrow} (MR_s, \beta, \gamma)
    \end{align}
    %
    and the corresponding tangent lifted action is given by
    %
    \begin{align}
    T \mathop{\mathbb{SO}(3)} \times TQ \mathop{\rightarrow} TQ \;\;\;   (v_{R_s}, v_{\beta}, v_{\gamma})  \mathop{\rightarrow}
    (Mv_{R_s}, v_{\beta}, v_{\gamma})
    \end{align}
    %
    This action is chosen based on the symmetry in the system;
    in this case, the fact that the kinetic energy of the spacecraft in a potential field free space
    remains unchanged under rotational transformations.
    The gimbal and the rotor configuration variables
    are viewed in a {\it base space (or shape space)} and the rigid body
    orientation is viewed as a group variable in a {\it fiber space}, and with a few additional
    requirements, the model is
    amenable to a principal fiber bundle description. See \cite{bullo_modelling_ctrl}
    for more details on
    describing mechanical systems in a fiber bundle framework.
    The fiber bundle structure separates the
    actuation and orientation variables and proves beneficial and intuitive in control design.

    Based on the above model description, we identify the principal fiber bundle
    $(Q, B, \pi, G)$,
    where $Q = \mathop{\mathbb{SO}(3)} \times \mathbb{S}^1 \times \mathbb{S}^1$,
    $B = \mathbb{S}^1 \times \mathbb{S}^1 $ and $\pi: Q \mathop{\rightarrow} B$ is a bundle projection map.
    %
    \begin{claim}
        %
        Under the defined group action, the kinetic energy of the total system
        remains invariant.
        %
    \end{claim}
    %
    \proof
    Straightforward.
    $\Box$.

    We now define
    a few geometric quantities on this fiber bundle on the lines of
    \cite{bloch_nonholo_mech_ctrl}.
    \begin{itemize}

    \item
    The {\it infinitesimal generator} of the Lie algebraic
    element $\hat{\eta} \in \mathfrak{so(3)}$ under the group action is the vector field
    %
    \begin{align}
    %
    \hat{\eta}_{Q}(q) = \frac{d}{dt}|_{t=0} (\exp(\hat{\eta}t) R_s, (\beta, \gamma)) =
    (\hat{\eta}R_s, (0, 0))
    %
    \end{align}
    %
    \item The {\it momentum map} $J : TQ \mathop{\rightarrow} \mathfrak{so(3)}^*$ is given by
    %
    \begin{align}
    %
    [J(q, v_q), \xi] = \inprod{ v_q   }{  \hat{\xi}_Q(q) }_{\mathbb{G}}
    %
    \end{align}
    %
    and
    since the kinetic energy is invariant under the action of the $\mathop{\mathbb{SO}(3)}$ group, we have
    %
    \begin{align}
    %
    \inprod{ v_q   }{  \hat{\xi}_Q(q) }_{\mathbb{G}} = \inprod{ v_{(e,(\beta,\gamma))} }
    {(R_s^T \hat{\xi} R_s,(0,0))  }_{\mathbb{G}}
    %
    \end{align}
    %
    which yields
    %
    \begin{align}
    %
    [J(q, v_q), \hat{\xi}] =  \inprod{Ad_{R_s^T}^* [( (\mathbb{I}_{gr})_s + \mathbb{I}_{s}) \Omega_s + R_{\beta} \mathbb{I}_{gr} \pmat{ 0  \\  \dot{\beta}
            \\  \dot{\gamma} }   ] }{\xi}
    \end{align}
    %
    where $\inprod{\cdot}{\cdot}$ denotes the inner product, while
    $[\cdot, \cdot]$ denotes the primal-dual action of the vector spaces $\mathfrak{so(3)}$ and
    $\mathfrak{so(3)}^*.$
    In the absence of external forces, the momentum map is conserved.
    Since the total spatial angular momentum of the system is constant, say $\mu$,
    the above expression
    yields
    %
    \begin{align}
    %
    \mu = Ad_{R_s^T}^* [( (\mathbb{I}_{gr})_s + \mathbb{I}_{s}) \Omega_s + R_{\beta} \mathbb{I}_{gr} \pmat{ 0  \\  \dot{\beta}
        \\  \dot{\gamma} }   ]
    \end{align}
    %
    \item
    The {\it locked inertia tensor} at each point $q \in Q$ is the mapping
    %
    \begin{align}  \mathbb I (q): \mathfrak{so(3)} \mathop{\rightarrow} \mathfrak{so(3)}^* \end{align}
    %
    and is defined as
    %
    \begin{align}  [ \mathbb I(q) \eta, \xi ] = \mathbb{G} (q) \left((\hat{\eta} R_s , (0,0)),
    (\hat{\xi} R_s , (0, 0))\right)
    %
    \end{align}
    %
    \item
    The {\it mechanical connection} is then defined as  the $\mathfrak{so(3)}$-valued one-form
    %
    \begin{align}

    \alpha: TQ \mathop{\rightarrow} \mathfrak{so(3)} \;\;\;\; (q, v_q) \mathop{\rightarrow} \alpha(q, v_q) = {\mathbb I(q)}^{-1} J(q,v_q)
    \end{align}
    %
    \end{itemize}
    %

           We now proceed to present a kinematic model and a dynamic model for the
    system under consideration.
    With the state-space as $X \stackrel{\triangle}{=} (R_s, (\beta, \gamma)) = (R_s, x)$, where $x \stackrel{\triangle}{=} (\beta, \gamma)$
    and defining $\tilde{\mathbb{I}}(x) =  (R_{\beta}  \mathbb{I}_{gr} R_{\beta}^T + \mathbb{I}_{s}) $, the control inputs
    (gimbal velocity and rotor spin)  at the kinematic
    level as $u \stackrel{\triangle}{=} \dot{x} = (\dot{\beta}, \dot{\gamma}) = \pmat{u_{\beta}  \\
        u _{\gamma} } $,
    the affine-in-the-control system model is
    %
    \begin{align}
    %
    \dot{X} = f(X) + g(X) u
    %
    \end{align}
    %
    where the drift and control vector fields are given by
    %
    \begin{align}
    f(X) = \pmat{R_s  \skew{ (  \tilde{\mathbb{I}}(x)^{-1} (Ad_{R_s}^* \mu))   }    \\  0 }
    \end{align}
    %
    \begin{align}
    %
    g_{\beta}(X) =  \pmat{- R_s  \skew{   (\tilde{\mathbb{I}}(x)^{-1}  (Ad_{R_\beta^T}^* (\mathbb{I}_{gr} i_2))  }
        \\
        \pmat{1  \\  0}   }
    \;\;\;\;\;
    g_{\gamma}(X) =  \pmat{- R_s  \skew{ (\tilde{\mathbb{I}}(x)^{-1}  (Ad_{R_\beta^T}^* (\mathbb{I}_{gr} i_3))  }
        \\
        \pmat{0  \\   1}     }
    %
    \end{align}
    %
    Here  $\skew{\cdot} : \mathbb{R}^3 \mathop{\rightarrow} \mathfrak{so(3)}$ is given by
    %
    \begin{align}
    %
    \skew{(\psi_1, \psi_2, \psi_3)} \stackrel{\triangle}{=}
    \pmat{ 0 &  - \psi_3  &  \psi_2  \\  \psi_3  &  0  &  -\psi_1  \\
        - \psi_2  &  \psi_1  &  0 }
    %
    \end{align}
    %

\section{The dynamic model}
To arrive at the dynamic model we proceed as follows.
From the expression for the total momentum
\begin{align}
\mu  & = Ad_{R_s^T}^* [ ((\mathbb{I}_{gr})_s + \mathbb{I}_{s}) \Omega_s + R_{\beta} \mathbb{I}_{gr} \pmat{ 0  \\  \dot{\beta}
    \\  \dot{\gamma} }   ] \nonumber   \\
& = R_s \pmat{ \tilde{\mathbb{I}}(x) & R_{\beta} \mathbb{I}_{gr}}  \pmat{\Omega_s
    \\  \pmat{ 0  \\  \dot{\beta}  \\  \dot{\gamma} }  }
\end{align}
We split the momentum in to two components - one due to the gimbal-rotor unit and the other due to
the rigid spacecraft. Further, we assume an internal torque $\tau_b$
(in the gimbal-rotor frame), generated by a motor,
acts on the gimbal and rotor unit. We then have, due to the principle of action and
reaction
\begin{align}
\frac{d}{dt} (R_s \mathbb{I}_{s} \Omega_s) = \underbrace{- R_s \tau_b}_{reaction}
\;\;\;\; \;\;
\frac{d}{dt} ( R_s [ R_{\beta} \mathbb{I}_{gr} R_{\beta}^T \Omega_s + R_{\beta} \mathbb{I}_{gr} \dot{x} ] )
= \underbrace{R_s \tau_b}_{action}
\end{align}
The detailed computation is now shown.
Differentiating
$
\mu=R_{s}R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})
$
with respect to time, we have
$\frac{d}{dt}\mu_{cmg}=\frac{d}{dt}\left\{ R_{s}R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\right\} =\text{torque acting on cmg external to cmg}$

$\tau_{extcmg}=\left\{ \begin{array}{c}
(R_{s}\hat{\Omega}_{s})R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\\
+R_{s}(R_{\beta}\hat{i}_{2}\dot{\beta}) \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\\
+R_{s}R_{\beta} \mathbb{I}_{gr} (-\hat{i}_{2}R_{\beta}^{T}\dot{\beta}\Omega_{s})\\
+R_{s}R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\dot{\Omega}_{s})\\
+R_{s}R_{\beta} \mathbb{I}_{gr} (\begin{bmatrix}0\\
\ddot{\beta}\\
\ddot{\gamma}
\end{bmatrix})
\end{array}\right\} $

\begin{align*}\tau_{extcmg}={} & R_{s}\hat{\Omega}_{s}R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\\
&+R_{s}R_{\beta}\left\{ \hat{i}_{2}\dot{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})+ \mathbb{I}_{gr} (-\hat{i}_{2}R_{\beta}^{T}\dot{\beta}\Omega_{s})+ \mathbb{I}_{gr} (\begin{bmatrix}0\\
\ddot{\beta}\\
\ddot{\gamma}
\end{bmatrix})\right\}
\end{align*}

In the spacecraft body coordinates,

\begin{align*}\tau_{extcmg}^{\mathcal{B}}={}&\hat{\Omega}_{s}R_{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\\
&+R_{\beta}\left\{ \hat{i}_{2}\dot{\beta} \mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})+ \mathbb{I}_{gr} (-\hat{i}_{2}R_{\beta}^{T}\dot{\beta}\Omega_{s})+ \mathbb{I}_{gr} (\begin{bmatrix}0\\
\ddot{\beta}\\
\ddot{\gamma}
\end{bmatrix})\right\}
\end{align*}
Defining two vectors
\begin{align*}
u_{1}={} &\mathbb{I}_{gr} (R_{\beta}^{T}\Omega_{s}+\begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix})\\
u_{2}={} &\left(\hat{i}_{2} \mathbb{I}_{gr} - \mathbb{I}_{gr} \hat{i}_{2}\right)R_{\beta}^{T}\Omega_{s}\dot{\beta}+\hat{i}_{2} \mathbb{I}_{gr} \begin{bmatrix}0\\
\dot{\beta}\\
\dot{\gamma}
\end{bmatrix}\dot{\beta}+ \mathbb{I}_{gr} (\begin{bmatrix}0\\
\ddot{\beta}\\
\ddot{\gamma}
\end{bmatrix})
\end{align*}
in the gimbal frame $\mathcal{G}$ such that
$\tau_{extcmg}^{\mathcal{B}}=\hat{\Omega}_{s}R_{\beta}u_{1}+R_{\beta}u_{2}$
. The second component of this vector gives the torque acting on the gimbal motor
and the third gives the torque acting on the wheel motor.
We now simplify this expression to obtain more explicit equations, which we then
compare with a standard model existing in the literature.
\[
[ \hat{\Omega}_s \tilde{\mathbb{I}}(x) \Omega_s  +  \tilde{\mathbb{I}}(x) \dot{\Omega}_s ]
\]
\begin{align}
= (-1)\hat{\Omega}_s R_{\beta} \mathbb{I}_{gr} \dot{x} - \dot{\beta} R_{\beta} {\cal U} R_{\beta}^T
\Omega_s - \dot{\beta} R_{\beta} \hat{i}_2 \mathbb{I}_{gr} \dot{x} - R_{\beta} \mathbb{I}_{gr}
\ddot{x}
\end{align}
where ${\cal U} \stackrel{\triangle}{=} \hat{i}_2 \mathbb{I}_{gr} - \mathbb{I}_{gr} \hat{i}_2$ is a symmetric matrix.

\section{Comparison to the Schaub-Rao-Junkins model}

We now draw connections between the approach outlined in the previous sections
with that of  the classical CMG modeling and analysis done in the Newtonian
framework in \cite{schaub_feedback_1998}, which is
cited in much of the aerospace literature. We shall refer to this paper as the SRJ paper
henceforth. We first relate the notation and then establish a
connection with the main equations of the SRJ paper.

The two primary variables in the SRJ paper and ours are related as in table \ref{tab:notationcomparison}.
\begin{table}[h]
\caption{\label{tab:notationcomparison} Comparison of notation with SRJ paper}
\begin{ruledtabular}
    \begin{tabular}{ccc}
        Variable                   & This paper     & SRJ paper\\ \hline
        Gimbal angle               & $\beta$        & $\gamma$ \\
        Rotor spin magnitude       & $\dot{\gamma}$ & $\Omega$ \\
        Satellite angular velocity & $\Omega_s$     & $\omega$ \\
    \end{tabular}
\end{ruledtabular}
\end{table}

The rotation matrix in the SRJ paper, relating the gimbal and spacecraft-body frame,
is described in terms of three orthogonal column vectors
of unit norm, $\{ \hat{g}_s, \hat{g}_{t}, \hat{g}_g \}$, where the subscripts $s, t$ and
$g$ correspond to the {\it spin, transverse and gimbal} axes,  as
\begin{align} \pmat{| & | & |  \\  \hat{g}_s & \hat{g}_{t} & \hat{g}_g  \\ | & | & |  \\ }
\end{align}
and further,
\begin{align}
\pmat{ \inprod{\hat{g}_s}{\omega} \\  \inprod{\hat{g}_{t}}{\omega}  \\
    \inprod{\hat{g}_{g}}{\omega}    } = \pmat{  \omega_s  \\ \omega_t  \\  \omega_g }
\end{align}
In our convention, the following correspondence holds:
\begin{align}
R_{\beta} =
\pmat{| & | & |  \\  \hat{g}_t & \hat{g}_{g} & \hat{g}_s  \\ | & | & |  \\ }
\end{align}
and
\begin{align}
R_{\beta}^T \Omega_s \longrightarrow
\pmat{  \omega_t  \\ \omega_g  \\  \omega_s }
\end{align}
The SRJ equation of motion (eqn. 28) written partially in terms of our notation is
\begin{align}
\tilde{\mathbb{I}}(x) \dot{\Omega}_s + \hat{\Omega}_s \tilde{\mathbb{I}}(x) \Omega_s =
\end{align}
\begin{align}
- \hat{g}_s [ J_s (\ddot{\gamma} + \dot{\beta} \omega_t)  - (J_t - J_g) \omega_t
\dot{\beta} ]
- \hat{g}_t [ J_s( \dot{\gamma} + \omega_s) \dot{\beta} - (J_t + J_g)
\omega_s \dot{\beta}  + J_s \dot{\gamma} \omega_g ]
- \hat{g}_g [ J_g \ddot{\beta}  -  J_s \dot{\gamma} \omega_t ]
\end{align}
while the RHS of the same equation in our notation is
\[
- [ \hat{\Omega}_s + \dot{\beta} \hat{i}_2 ]  R_{\beta} \mathbb{I}_{gr} \dot{x}
- \dot{\beta} R_{\beta} ( \hat{i}_2 \mathbb{I}_{gr} - \mathbb{I}_{gr} \hat{i}_2 ) R_{\beta}^T \Omega_s
- R_{\beta} \mathbb{I}_{gr} \ddot{x}
\]
\[
=  - \hat{g}_t [ (J_z + I_s) \dot{\gamma} \dot{\beta}  - (J_x + I_g) \dot{\beta} \omega_s
+ (J_z + I_s) \dot{\gamma} \omega_g + (J_z + I_s)  - (J_x + I_t) \dot{\beta} \omega_s]
\]
\[
- \hat{g}_g [ (J_x + I_g) \ddot{\beta} - (J_z + I_s) \dot{\gamma} \omega_t ]
\]
\[
- \hat{g}_s [ (J_z + I_s) \ddot{\gamma}  + (J_x + I_g) \dot{\beta} \omega_t  +
((J_z + I_s) - (J_x + I_t) ) \dot{\beta} \omega_t ]
\]
\\ \vspace{1in}
The terms in the model expand as shown below.
\begin{align*}
R_{\beta} \mathbb{I}_{gr} [0,\ddot{\beta},\ddot{\gamma}]^{T} & =\vec{g}_{g}(J_{x}+I_{g})\ddot{\beta}+\vec{g}_{s}(J_{z}+I_{s})\ddot{\gamma}\\
R_{\beta}\hat{i}_{2}\dot{\beta} \mathbb{I}_{gr} [0,\dot{\beta},\dot{\gamma}]^{T} & =\vec{g}_{t}(J_{z}+I_{s})\dot{\gamma}\dot{\beta}\\
\hat{\Omega}_{s}R_{\beta} \mathbb{I}_{gr} [0,\dot{\beta},\dot{\gamma}]^{T} & =\begin{array}{c}
\vec{g}_{s}((J_{x}+I_{g})\dot{\beta}\omega_{t})+\vec{g}_{g}(-(J_{z}+I_{s})\dot{\gamma}\omega_{t})\\
\vec{g}\left(-(J_{x}+I_{g})\dot{\beta}\omega_{s}+(J_{z}+I_{s})\dot{\gamma}\omega_{g}\right)
\end{array}\\
\hat{i}_{2} \mathbb{I}_{gr} - \mathbb{I}_{gr} \hat{i}_{2} & =
\begin{bmatrix}0 & 0 & \left(J_{z}+I_{s}-(J_{x}+I_{t})\right)\\
0 & 0 & 0\\
\left(J_{z}+I_{s}-(J_{x}+I_{t})\right) & 0 & 0
\end{bmatrix}\\
R_{\beta}(\hat{i}_{2} \mathbb{I}_{gr} - \mathbb{I}_{gr} \hat{i}_{2})R_{\beta}^{T}\Omega_{s}\dot{\beta} & =(\vec{g}_{t}\omega_{s}+\vec{g}_{s}\omega_{t})(\left\{ J_{z}+I_{s}-(J_{x}+I_{t})\right\} \dot{\beta})
\end{align*}

\section{Connection form}
We now detail the explicit computation of the connection form.
The principal fiber bundle structure introduces a vertical space in the tangent space at
each point on the manifold. The vertical space consists of those vectors corresponding to
the infinitesimal generator vector fields at that particular point.
The tangent space is then expressed as the direct sum of the vertical
space and a horizontal space, where the
horizontal space gets defined as the subspace orthogonal to the vertical space in the
inner product induced by the Riemannian metric.
\begin{definition}
    %

    A principal connection on $Q = (M,G,\pi)$ is a $\mathfrak{g}$ valued 1-form $\mathcal{A}$ on $Q$ satisfying,
    \begin{enumerate}
        \item $\mathcal{A}(\xi_{Q}(q)) = \xi$, $\forall \xi \in \mathfrak{g}$ and $q \in Q$;
        \item $\mathcal{A}(\Phi_{g \ast}X_{p}) = Ad_g^* (\mathcal{A}(X_{p}))$ for all $X_{p} \in TQ$
        and for all $g \in G$. This is called the equivariance of the connection.
    \end{enumerate}
\end{definition}
The expression for the kinetic energy  is
\[
[\Omega^{T}\ u_{1}\ u_{2}]
\begin{bmatrix}
\mathbb{I}_{s} + R_{\beta} \mathbb{I}_{gr} R_{\beta}^{T} & (J_x + I_g)\vec{g} & (J_z + I_s)\vec{s}_{\beta}\\
(J_x + I_g)\vec{g}^{T} & (J_x + I_g) & 0\\
(J_z + I_s)\vec{s}_{\beta}^{T} & 0 & (J_z + I_s)
\end{bmatrix}
\begin{bmatrix}\Xi\\
w_{1}\\
w_{2}
\end{bmatrix}
\]

Action and infinitesimal generator are as shown in other sections.
So vertical space at a point
$q$ is spanned by
$\{(\square,0,0)|\square\in T_{q}SO(3)\}$. Locally we can represent elements in
$T_{q}Q$ as
$((r_{1},\ r_{2},\ r_{3}),\ \dot{\beta},\ \dot{\gamma})$ where
$(r_{1},\ r_{2},\ r_{3})\in\mathbb{R}^{3}\simeq\mathfrak{so}(3)$.Then

\[
V_{q}Q=\mathrm{span}\{\frac{\partial}{\partial r_{1}},\ \frac{\partial}{\partial r_{2}},\ \frac{\partial}{\partial r_{3}}\}
\]

To find,
$H_{q}Q$, the $\mathbb{G}$ orthogonal space has to be found out.

\[
\left\langle \begin{bmatrix} \mathbb{I}_{s} +R_{\beta} \mathbb{I}_{gr} R_{\beta}^{T} & (J_x + I_g)\vec{g} & (J_z + I_s)\vec{s}_{\beta}\\
(J_x + I_g)\vec{g}^{T} & (J_x + I_g) & 0\\
(J_z + I_s)\vec{s}_{\beta}^{T} & 0 & (J_z + I_s)
\end{bmatrix}\begin{bmatrix}\begin{pmatrix}h_{1}\\
h_{2}\\
h_{3}
\end{pmatrix}\\
h_{4}\\
h_{5}
\end{bmatrix},\quad\begin{bmatrix}\square\\
0\\
0
\end{bmatrix}\right\rangle =0
\]
where
$\square\in V_{q}Q$
.
This implies
\[
(\mathbb{I}_{s} +R_{\beta} \mathbb{I}_{gr} R_{\beta}^{T})\begin{pmatrix}h_{1}\\
h_{2}\\
h_{3}
\end{pmatrix}+ (J_x + I_g) \vec{g}h_{4} + (J_z + I_s)\vec{s}_{\beta}h_{5}=0
\]

The horizontal vector
$(h_{1}\ h_{2}\ h_{3}\ h_{4}\ h_{5})^{T}$
satisfies 3 (independent) equations in 5 variables.
The horizontal space is then 2 dimensional as expected since the number
of shape variables is 2.
If we let
$h_{4}$ and
$h_{5}$ be the independent variables, then
\begin{align*}
\begin{pmatrix}h_{1}\\
h_{2}\\
h_{3}
\end{pmatrix}= & (\mathbb{I}_{s} +R_{\beta} \mathbb{I}_{gr} R_{\beta}^{T})^{-1}
[(J_x + I_g)\vec{g}\ (J_z + I_s)\vec{s}_{\beta}]
\begin{pmatrix}h_{4}\\
h_{5}
\end{pmatrix}\\
= & \tilde{I}_{\beta}^{-1}
[(J_x + I_g) \vec{g}\ (J_z + I_s) \vec{s}_{\beta}]
\begin{pmatrix}h_{4}\\
h_{5}
\end{pmatrix}
\end{align*}

Now we can write any tangent vector as the sum of a vertical vector and
a horizontal vector as follows

\[
v_{q}=\begin{pmatrix}v_{1}\\
v_{2}\\
v_{3}\\
0\\
0
\end{pmatrix}+\begin{bmatrix}\tilde{I}^{-1}
[(J_x + I_g) \vec{g}\ (J_z + I_s) \vec{s}_{\beta}]\\
\begin{array}{cc}
1 & 0\\
0 & 1
\end{array}
\end{bmatrix}\begin{pmatrix}h_{4}\\
h_{5}
\end{pmatrix}
\]

The $\mathfrak{g}$ valued connection form can be then written (locally) as (here we write it as
$\alpha:TQ\rightarrow\mathfrak{so}(3)\simeq\mathbb{R}^{3}$)

\[
\begin{bmatrix}\alpha_{11} & \alpha_{12} & \alpha_{13} & \alpha_{14} & \alpha_{15}\\
\alpha_{21} & \alpha_{22} & \alpha_{23} & \alpha_{24} & \alpha_{25}\\
\alpha_{31} & \alpha_{32} & \alpha_{33} & \alpha_{34} & \alpha_{35}
\end{bmatrix}\left(\begin{pmatrix}v_{1}\\
v_{2}\\
v_{3}\\
0\\
0
\end{pmatrix}+\begin{bmatrix}\tilde{I}_{\beta}^{-1}[(J_x + I_g) \vec{g}\ (J_z + I_s) \vec{s}_{\beta}]\\
\begin{array}{cc}
1 & 0\\
0 & 1
\end{array}
\end{bmatrix}\begin{pmatrix}h_{4}\\
h_{5}
\end{pmatrix}\right)=\begin{pmatrix}v_{1}\\
v_{2}\\
v_{3}\\
0\\
0
\end{pmatrix}
\]
solving we get,
\[
\begin{bmatrix}\alpha_{11} & \alpha_{12} & \alpha_{13} & \alpha_{14} & \alpha_{15}\\
\alpha_{21} & \alpha_{22} & \alpha_{23} & \alpha_{24} & \alpha_{25}\\
\alpha_{31} & \alpha_{32} & \alpha_{33} & \alpha_{34} & \alpha_{35}
\end{bmatrix}=\begin{pmatrix}\mathrm{Id}_{3\times3}\quad & -\tilde{I}_{\beta}^{-1}
[(J_x + I_g) \vec{g}\ (J_z + I_s)\vec{s}_{\beta}]\end{pmatrix}
\]
\section{Conclusions}
We present the spacecraft system with the variable speed control moment gyros (VSCMG)
cast into a geometric framework based on the principal fiber bundle.
The dynamics of the system are derived.
A kinematic and dynamic model for the above system is presented here.
The expressions for the associated geometric objects such as the
kinetic energy metric, locked inertia tensor,
momentum map and mechanical connection are derived.
The symmetry in the system is used to find the conserved quantity and
reduce the number of state variables in the system.
The corresponding reconstruction equations are derived.

\section*{References}
\bibliographystyle{aiaa}

redpajama_set_name: RedPajamaArXiv


text:
Q: User inputted array is entirely the last input When I execute this program, the canidateArray only stores the last user input as every variable in the array.
import java.util.Arrays;

import java.util.Collections;

import java.util.Scanner;

public class ArrayElection {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner input = new Scanner(System.in);
        System.out.println("Enter the number of candidates: ");
        int loops = input.nextInt();
        int loops2 = loops;
        Canidate[] canidateArray = new Canidate[loops];
        String canidatename;
        int canidatevotes = 0;
        int outputno = 1;
        while (loops > 0){
            System.out.println("Enter " + outputno +". name:");
            canidatename = input.next();
            System.out.println("Enter votes:");
            canidatevotes = input.nextInt();
            new Canidate(canidatename, canidatevotes);
            loops = loops - 1;
            outputno = outputno + 1;
        }

        if (canidateArray[0].getVotes() == canidateArray[1].getVotes()) {
            System.out.println("The election is a tie between the following candidates: ");
            System.out.println(canidateArray[0].getName() + " (" + canidateArray[0].getVotes() + " votes)");
            System.out.println(canidateArray[1].getName() + " (" + canidateArray[1].getVotes() + " votes)");
            System.out.println(canidateArray[2].getName() + " (" + canidateArray[2].getVotes() + " votes)");
        }
        else {
            System.out.println("The winner is " + canidateArray[0].getName() + " with " + canidateArray[0].getVotes() + " votes!");
        }

    }
    public static class Canidate {
        private static String name;
        private static int votes;

        public Canidate(String name, int votes) {
            this.name = name;
            this.votes = votes;
        }

        public static String getName() {
            return name;
        }
        public static int getVotes() {
            return votes;
        }
    }
}

A: You don't store anything in the array. Fix :
    while (loops > 0){
        System.out.println("Enter " + outputno +". name:");
        canidatename = input.next();
        System.out.println("Enter votes:");
        canidatevotes = input.nextInt();
        loops = loops - 1;
        canidateArray[outputno-1] = new Canidate(canidatename, canidatevotes);
        outputno = outputno + 1;
    }

But you'll have to fix your last part of code. You test canidateArray[0] vs canidateArray[1] while you can have

*

*1 candidate, then it will trigger an IndexOutOfBoundsException

*or more than 2 candidates

redpajama_set_name: RedPajamaStackExchange


text:
'Revenge' Returned Much Darker & Packed With Shocking Revelations
By Christine DiStasio
The new 10pm time slot is going to do wonders for Revenge. The ABC drama returned Sunday night with a packed episode that left us scratching our heads. This isn't the Revenge that aired two months ago, but that might actually be a good thing. The show debuted at its new time, 10pm, on Sunday night and it's clear that the freedom that comes with airing later in the primetime block is really going to shake things up.
Before we broke for a painfully long time, Emily Thorne was just about recovered from Daniel Grayson shooting her on their wedding night. Other than that — Daniel had had an affair with Sarah, Patrick had found his birth father (and found out he was a child of rape), and Niko learned that Aiden was the one who killed her father, Takeda. Thankfully, on Sunday night we were finally able to forget about Sarah's annoying and pointless storyline to focus on things that were even juicier — here's your guide to Revenge's shocking return episode:
Emily's Blackouts Are Most Powerful Than We Thought
At the end of the show's previous episode, Emily woke up in Conrad's hotel room — with no idea of how she got there and why. And those blackouts are getting a hell of a lot worse. On Sunday night, we learned that during the particular blackout that led her to Conrad, Emily also called the first Mrs. Grayson and told her that she wanted her help with a divorce. (Stevie Grayson is a high-powered divorce attorney for the rich and famous.) She also told her that she was in love with someone else — so Blackout Emily is apparently Truth-Talking Emily.
The remainder of Sunday night's episode fly by in a blur — literally. It was impossible to discern whether or not Emily was in blackout mode as she slipped in and out of it all night. First, Blackout Emily showed up and tried, aggressively, to hook up with Aiden — who basically told her to back off. Then, Nolan found Blackout Emily sleeping on the front porch of her old house with no recollection of the past 24 hours. And, according to Emily's doctors, the abnormality in her CAT scan isn't an explanation for the blackouts — but you'll never guess what is.
According to Nolan, Emily's mother suffered her first psychotic break (she tried to down Emily) at her age and Emily might be following in her footsteps. It would make sense, considering that Emily's getting violent and it's almost as if her brain is turning against her. Or as Nolan put it — her mind isn't on board with the revenge plan anymore and now it's trying to sabotage Emily.
Patrick KILLED HIS FATHER
Patrick burned down the gallery during the show's last episode and he hired his rapist father to do the electrical repairs — much to Victoria's dismay. So, why hire the guy that raped your mother that you love so much? So he can kill him — an idea that Victoria immediately tried to squash but it ended up going down anyway.
He and Patrick chat it up while he does repairs in the gallery and Patrick debates whether or not it'd be a great idea to electrocute him to death. (He ultimately decides not to.) And it actually seems like he might be feeling a desire to get to know his birth father. Well, that's short-lived. When his father shows up at Grayson Manor during Charlotte's birthday party, the shit really hits the fan.
Victoria flies over to the gallery like a bat out of hell to reprimand Patrick for not firing his father like she commanded earlier in the episode. Patrick's like, "sorry I'm not sorry, mom," and tries to explain himself when his father shows up. And it immediately becomes clear that he is totally not a changed man. He advances like a predator on Victoria and Patrick and in the blink of an eye, Patrick hits him over the head and he's on the floor bleeding profusely from his skull. He begs for help and Victoria, in a powerful moment, repeats his words back to him, "Relax, Honey." The same words he said to her before he raped her when she was 15 years old. WELL, SHIT, REVENGE.
Victoria and Patrick decide not to call the cops or 911 and instead just watch him die. So now what, guys?
Stevie Grayson Is Jack's Mom
WHAT THE HELL. Stevie Grayson hung around the Stowaway a lot on Sunday night's episode and dropped subtle hints that it used to be her favorite place. But, apparently, it wasn't because they had great drinks and it was off the Hamptons' beaten path. The real reason why the first Mrs. Grayson loved that bar so much — she had an affair with Jack's father AND JACK IS HER SON.
In the last few minutes of Sunday night's episode, Stevie revealed that she's the rightful owner of Grayson Manor and promptly headed over to the Stowaway to ask Jack to share the stories about Conrad he alluded to earlier in the episode. When Jack asks why she's so interested in chatting about his father, the Stowaway, and how Conrad was so terrible to him she drops a shocker — "JACK, I AM YOUR MOTHER." (Well, not in those exact words, but it sounds more dramatic that way.) And we're off on another paternity scandal.
We're definitely not disappointed that Revenge moved to 10pm if Sunday night's episode is any indication of where the show's third season is headed. Things are going to get really dark in the Hamptons and we like it.

redpajama_set_name: RedPajamaCommonCrawl


text:
The Lounge was a New Zealand Television talkback show hosted by Katie Kouloubrakis and filmed in Christchurch. The show was broadcast on Cue TV/Sky 110 and could also be viewed online on Freeview and the show's website. The show had been running since 3 September 2007. The show's broadcaster, Cue TV, became defunct on 31 May 2015.

The show featured a variety of interviews and segments with topics such as gardening, cooking, fashion, interior design and theatre in New Zealand.

References

External links
 Official Lounge TV website
 Freeview site
 Cue TV site

New Zealand television talk shows
Cue TV original programming

redpajama_set_name: RedPajamaWikipedia


text:
"Generations" Fall of Cybertron Vortex Toy Review
Retailer: General Release (Toys R Us, Target, Wal-Mart etc.)
Accessories: Swords x 2
*Images above with asterisks(*) and text in italics below from The Official Transformers web site:
Few AUTOBOTS fear a fight against VORTEX. What they fear is being captured and at his mercy. He uses magnetic grapples to haul helpless captives high into the sky. There he treats them to a terrifying series of swoops, loops and dives before dropping them to their doom.
This high-flying DECEPTICON warrior is big trouble for the AUTOBOTS all by himself, but he's also part of something a lot bigger – and scarier! Your VORTEX figure comes with awesome firepower, and he can convert to Cybertronian assault chopper mode and back whenever the battle calls for it. But when it's time to bring overwhelming force against his AUTOBOT enemies, he can combine with other COMBATICONS (sold separately) to form a giant DECEPTICON BRUTICUS robot figure! His weapon combines with other COMBATICON weapons to form DECEPTICON BRUTICUS's sonic cannon! Get one piece of an invincible DECEPTICON BRUTICUS warrior with this hardcore VORTEX figure!
Robot-to-vehicle warrior! Converts to Cybertronian assault chopper vehicle mode! VORTEX figure combines with other COMBATICON figures (sold separately) to build a giant DECEPTICON BRUTICUS robot! Figure becomes an arm or leg! Collect all 5! Includes VORTEX figure and accessories. Deluxe Class Series 1 006 VORTEX. Ages 5 and up.
2012's big "Transformers" multimedia event was not a movie, but rather a video game. Following up on the success of "War for Cybertron", High Moon Studios was due to release "Fall of Cybertron" in August of 2012 so a large portion of the "Generations" toy line became dedicated to characters and designs from the game itself. One of the key characters in the game is Bruticus, the Combiner giant formed by the team known as "The Combaticons". One of their members, the always scheming Swindle was part of this release.
The existence of a new Bruticus figure caused quite a stir among fans. For years we've wanted a new Combiner figure, and lucky for the fandom at large we now have one. Even better? This guy was composed of five Deluxe Class figures, each one with its own unique transformation and identity. Before the initial retail release of this figure, the summer of 2012 saw the release of the entire set in a special box (with different colors)as a San Diegeo Comic-Con exclusive. This guy sold out within minutes of being available on Hasbrotoyshop and by the following week went for easily double the price on ebay. No doubt, this is one figure tons of Transformers fans wanted!
However, those fans who did not attend San Diego Comic-Con would also get a chance to purchase Vortex (and the other Combaticons) at mass retail several months later. In October 2012, the Combaticon team was released as one wave to mass retail. Each of these figures featured new decos that were intended to be brighter and more "eye catching" on toy store shelves. This review will focus on the changes made to Vortex for this release. Check out my previous Vortex review for a closer look at the figure's sculpt and mold.
It's kind of funny, in my previous Vortex review I had ended it by saying the color scheme mystified me a bit because it really had nothing to do with any previous Vortex color scheme. The closest tie I can think of would be to the Wal-Mart exclusive "desert camo" version of "Ro-Tor" from "Robots in Disguise" (which used the G1 Vortex sculpt) but that's about it. Now I begin this review by scratching my head once again and wondering - where did these colors come from?!
This time around, Vortex is mostly cast in red and lavender plastic. Some smaller parts are black (such as his elbow joints), but those two colors are the most striking on the figure. Red makes up most of the armor panels around the center of the robot including his arms, lower legs and back. The center of the robot is mostly focused on the lavender plastic, which forms parts such as his head, chest and the rotor blade weapon on his left arm. The colors chosen are not ultra bright in shade, but together definitely have a dramatic effect. The blades of the weapons have been painted yellow and the hilts are red, but you can still see some of the base lavender plastic sticking out.
Just as you're settling into the idea of red and lavender being the primary colors on Vortex, your eyes will get walloped by the neon yellow and red paint colors used on the figure. Red outlines the chest in the same way brown was used on the SDCC version. Yellow is pinted onto the eyes and thin strips on his chest, making it look almost like he has two gigantic eyes on his chest (it's a bit unsettling). Black paint is found on the lower legs, where they fill in color for the vehicle mode windows. It's also used to paint the hands, which is a small but important detail. Bits of lavender paint are scattered about here and there such as the edges of the forearms and small details on the feet. Some areas that were painted on the SDCC version (including the shoulders and waist cover piece) have been left unpainted, but those were minor enough details that I didn't really notice until I did a side by side comparison. It's not unexpected for the mass release figure to have less deco applications than the SDCC exclusive so this isn't a big deal as far as I'm concerned. I like the colors overall and they work well together, but nothing about them scream "Vortex" to me.
All of Vortex's joints are tight and his weapons can attach to his hands without a problem. His rotor blade also spins well when pushed, but you may have to angle the forearm out a little to get the full effect.
Detach the weapons and set them aside for now.
Push the robot head (and the platform it is on) back.
Swing the back panel (the tail of the helicopter) up.
Rotate the waist around.
Swing the robot arms back and fold the forearms against the upper arms.
Swing each arm up on the piece connected to the shoulders.
Rotate the base of the helicopter blades to the center and splay them out.
On each lower leg piece, swing the skids for the vehicle mode out.
On the inside of the right leg, swing out the blaster weapon.
Fold both legs back and connect them together.
Attach the weapons to the sides of the skids.
In vehicle mode, Vortex's red color really stands out as the primary focus of his deco. This is largely due to all his armor panels coming together and hiding a lot of the contrasting lavender parts from the robot mode. There is still some of the lavender color however, mostly found on the rotor and the base of the rotor. The figure isn't one note by any means however. The weapon mounted on the front nose is black and some of the black parts for the Bruticus limb mode can be seen sticking out from the bottom of the figure. Lavender paint is used in a slightly irregular pattern that runs from the front to the back of the vehicle on the sides (though it breaks where his skids are). The lavender is also used on the skids themselves towards the front. In contrast to these brighter colors, black is used to paint the windows of the vehicle. This matches up nicely with the weapon mounted in front and helps tone down the figure a bit. Overall, I have to say I do like the color scheme, but I'm mystified by it at the same time since it's not very "combat" like (no dark tones, camo patterns etc.) and it doesn't really homage any pre-existing version of Vortex.
Functionally speaking the rotor on the figure can spin freely in this form and you can attach extra weapons to Vortex's own blade weapons to create more powerful configurations.
Leg Mode:
In the Generation One series, Vortex often formed an arm for Bruticus, even though his toy had the ability to form either an or a leg. With this iteration of the character, he can form a leg for the Combiner giant. Start with Vortex in vehicle mode. Split the cockpit section in the middle and swing in the machine gun. On the underside of the vehicle, grab hold if the brown part in the middle and pull it forward on the central hinge, elongating the body of the vehicle. Now swing each of the cockpit halves up and put them together. Push the tail of the vehicle forward to reveal the connection point and plug it into Onslaught (the side doesn't matter).
Thanks to the relative bulk of the vehicle mode's front end and the skids out to the sides, Bruticus gets one solid and stable leg from Vortex. I think the use of the armor "skirt" as a heel piece is brilliant and works really nicely to help keep the giant from falling back. I also really like the look of the rotor blades opened up and facing front. In this form the skids are facing forward and you can attach weapons to them, but since they're right on the ground they'll have to be relatively smaller or thinner weapons such as some of the hand weapons included with Human Alliance Commander Class figures.
Arm Mode:
Start with the figure in vehicle mode, then split the cockpit section open and swing in the machine gun. On the left half of the cockpit is the hand. Swing the hand out and move the thumb to the left or right depending on which arm you are going to make Vortex into. Extend the middle section just like you would for the leg mode. Rotate the forearm section around (depending on which side you are forming). On the underside of the vehicle mode's tail, push the connection piece down, then attach it to Onslaught's shoulder joint.
Vortex's arm mode works out to be very similar to his Generation One arm mode. The rotor blades stick out to the sides, the tail of the vehicle becomes the upper part of the arm and the front part of the vehicle becomes the portion where Bruticus' hand is attached (though in G1 it was a completely different piece that you attached separately). Unlike his G1 counterpart, Vortex is actually able to bend at the elbow area when combined with the other Combaticons. Also, despite its "open palm" position, the hand is designed to hold a weapon. Need more weaponry attached? The skids face front here, and you could easily attach more weapons them. Porportionally the figure looks great.
I can't in good conscience say that this is a bad figure. I like it in all its modes and it's fun to play with. The sculpt is cool and the colors are neat. My only problem with it is the color scheme doesn't say "Vortex" to me in any way, shape or form. It looks more like a semi-homage to "Robots in Disguise" Ro-Tor (and even that's a stretch). A good figure, but if you're a Generation One "stickler", it may bug you for the same reason it bugs me.
Note: After I posted this review, fellow fan Emanuele LaLota pointed out that this color matches up with the "Vortex" equivalent from the Energon "Bruticus Maximus" set. This makes total sense from a deco/homage perspective. Sadly, G1 fans are still shorted deco-wise on this sculpt.
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Gujarat Orbit
Select your choice Archeology in Gujarat Beaches in Gujarat Birds Sanctuaries in Gujarat Dams in Gujarat Pilgrims in Gujarat Fairs in Gujarat Museums in Gujarat Gardens in Gujarat Hill Stations in Gujarat National Parks in Gujarat Rivers in Gujarat WildLife Sanctuary in Gujarat Water Falls in Gujarat Festivals in Gujarat Historical Places in Gujarat
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Kutch Desert Wildlife Sanctuary
About Kutch Desert Wildlife
Nearest Attraction
Kutch Desert Wildlife Sanctuary -Kutch
Kutch Desert Wildlife Sanctuary of Gujarat has vast area of sun-baked mud flats that are salt impregnated. Some of the area around Kutch Desert Wildlife Sanctuary in Gujarat have small patches of uplands and the hilly islands of the sanctuary are called bets. Kutch Desert Wildlife Sanctuary has marine calcareous grit and oyster bed in the shore bordering the Arabian sea.Kutch Desert Wildlife Sanctuary in Gujarat houses some of the rare wild animals like striped hyena, porcupine, fox, small Indian civet, Indian pangolin and a large number of reptiles. You will find both venomous and non-venomous snakes, monitor lizards, star tortoise in the Kutch Desert Wildlife Sanctuary at Gujarat. Some of the rare species of birds are found in the Kutch Desert Wildlife Sanctuary at Gujarat.
The sanctuary has some other attractions as well. Embedded below the Jurassic and Cretaceous rocks on Khadir, Kuvar and Pachchham bets, are plenty of fossils of vertebrates, invertebrates and plants. There are records of recovery of fossils of dinosaurs, crocodiles (of Dinosaurian period) and whales (of tertiary period). Fossilised forests have also been found in the rocks belonging to Jurassic and Cretaceous eras. The fossils of invertebrates include those of amonites, sea urchins and such others.
"The Little Rann of Kutch is the most desolate place on earth," says Malek. "When you're in the desert, you feel as thought you're standing in the middle of a plate. You can hear the silence. There's not a stone, not a tree, nothing at all…just the horizon, stretching for 360 degrees."Malek is also a talented naturalist. He explains a little about the endangered Wild Ass, the khur species of which is found only in the Little Rann of Kutch. "The wild ass is the only animal that can survive in these harsh conditions," he says. "It can survive on forage that wouldn't sustain even a goat, with a conversion rate of food to energy of over 95 per cent."
Buried city Dholavira of Harappan civilization was excavated here, which attracts hordes of archeologists here from all across the world. Equally enticing is the Flamingo City located in the mud flats of the Rann, about 10 km. from Nir out post on Kala Dungar. It is the only area where flamingoes breed regularly.Kachchh Desert Wildlife Sanctuary represents one of the largest seasonal saline wetland areas having water depth between 0.5 to 1.5 metres. But, after October-November, water dries up and the entire area turns into saline desert. The sanctuary supports wide variety of water birds and bewildering range of mammalian wildlife.
Besides the Indian Bustard, some of the other wild animals that you can feast your eye upon during your tour to Bustard Sanctuary, Kutch include Harriers, Eagles, Jungle Cat, Desert Cat, Chinkara and migratory birds. The best season to visit the Kutch Bustard Sanctuary is from late monsoon to winter. The nearest airport is at Bhuj which is at 110 km and the nearest railhead is the Naliya Railway Station which is 20 km from the sanctuary.
Location info:
Address:Kutch Desert Wildlife Sanctuary ,Kutch,Gujarat,India
District: Kutch
Nearest City: Bhuj
Best time to visit: October to March
Climate/Weather:
Weather of Kutch is tropical monsoon with an average annual rainfall of approximately 14 inches. In Summer temperature can reach up to 48°c. In Winter temperature ranges from 12 °c to 27 °c.
Set up in the year 1986, the Kutch Desert Wildlife Sanctuary is the largest of all the wildlife reserves of Gujarat and is a treat to the traveler on his tour to Gujarat. Spread over a sprawling 7506.22 sq.km it serves as shelter to a number of wild animals and birds. The Kutch Desert Wildlife Sanctuary is located on parts of the Great Rann of Kutch which is primarily extremely hot, dry and dusty zone.
Interesting things to do:
An interesting feature for adventure lovers is a jeep or camel safari in and across Rann of Kutch with tented camps on the baits. These trips add more thrill as they last for about a week.
For photography enthusiasts, special rides and camouflaged boats are provided
A trip to a typical Saurashtra village and an insight into the art of handloom weaving and Dyeing Units can be enticing due to the vibrantly colored dyes and the exquisite craftsmanship. The age old craft of pottery can also be viewed from close quarters.
Tribal life is best experienced with the tribal people and there is no substitute for a stay at the typical tent. These camps are organized between July and September.
Around the Wild Ass Wildlife Sanctuary, you may shop for Patola Silk Sarees, Bandhanis, Ghagra-cholis and marriage costumes. You will also find interesting wall hangings, embroidered quilts, cradle clothes,
Interesting things to Visit:
Animals:
The Kutch Desert Wildlife Sanctuary is inhabited by a wide variety of wild animals like hyenas, foxes, wolves, and chinkaras. Most of the mammals like the Nilgai, Wild Ass and the Black Buck which are seen in the Wild ass Sanctuary are also found here.
Nilgai
Chinkara
Indian Hare
Pale Hedgehog
Small Indian Civet
Indian Porcupine
Indian Fox
Birds:
The Kutch Desert Wildlife Sanctuary not only houses animals but birds as well. It is famous for being a home to the colorful flamingos in large numbers. Flamingos sporting a riot of rich and vibrant colors of dark red, yellow, blue are to be seen here. In fact the site is called Flamingo City near the Solanki Bet. Also, the reserve houses the White Pelican and the Avocet which have made this their breeding grounds. The Great Indian Bustard, Stolzca's Bushcat, painted sandgrouse, larks, tits, raptors, steppe eagle, tawny eagles and various water-fowls can be seen here.
Spoonbill
White backed vulture
Black vultures and more.
Flora:
There are two hills named- Kala Dungar and Goro Dungar. On this hilly island exist several microhabitats. They include grassland, scrubland, barren wasteland, agricultural land, village ponds, irrigation reservoir etc. All of them provide habitat to the fauna of one or the other type. Both the hills represent rocky habitats, with or without scrubs like-Prosopis chilensis, kahri jar, mithi jar, gugal, thor, lai, khijado, gorad, hermo baval, kerdo, bokhano etc
Wildlife:
Rann of Kutchh Wildlife Sanctuary of Gujarat is the only abode of Asiatic Wild Ass in India. The chestnut-brown animal is the last survivor of wild horse family of the Indian subcontinent and is found nowhere in the country except the Thar Desert of Gujarat. The other wildlife attractions of the Little Rann of Kutch Wildlife Sanctuary include Gazelle, Blue Bull, Wolf, Indian Foxes, Jackal, Jungle Cat, Hare, etc.
Kutch Desert Festival:
A visit to Kutch Desert Festival, offers access to the interior and beautiful recesses of the region of Kutch, situated in Gujarat, India. A visit to Kutch Desert Festival, offers an insight into the region which comprises of expansive wastelands and eerie landscapes to the excitement of a large number of tourists who come to visit Gujarat, situated in India. Kutch is a large inundated section of land bearing similarities with the American Wild West. Kutch, situated in Gujarat, India, can also be equated with a Desert in some terrains.
Mobile range info:
Nearest Railway Station:Ballarpur railway station
Nearest Airport:Bhuj and Kandla airports.
Road Transport:The sanctuary is well connected to the other important places in the state by State Transport Corporation buses as well as luxury coaches operated by private companies.The Rann of Kutch is accessible via Dasada village, 93 kms from Ahmedabad.
Nearest Visiting places:
Bhuj:
This is known as the famous walled city of the state, Bhuj has its great importance of ancient values and historical backgrounds to denote that it is one of the ancient spots in the country. The town wall is measured as 35ft high and 4ft thick, an unimaginable mega structure engineering those days have taken place, is now a history and talk of the town too. previously , Bhuj was the capital of the native state of Kutch, and this city was under the rule of Jadeja Rajputs till Independence.As this spot has various places of historical values such as old palaces and museums around, namely the museum of Gujarat, Prag Mahal, Aina Mahal, Sarad Bagh palace, Kutch museum. The most heart felt hall mark of this town is the 2001 earthquake the devastation that demolished almost all hope and pride of this town. Yet, Bhuj has its tourist values to be visited.
Anjar:
The major spots of tourist visit is the shrine of Jesai Toral and the bungalow of James Mcmurdo and the other spots of visit is Ajaypal temple and the holy shrine of Pinjora Pir are the locations of spirituality and serenity. The famous Jesai-Toral fair is organized here for a celebration of colorful culture in the district. Anjar is famously known for its block printing works, nutcrackers, scissors and penknives manufacturing
Bela:
This spot is in the borders of Rann of Kutch which is a famous for its wild ass sanctuary. It is a hill station named Nilva. Nature and nature everywhere would mesmerize everyone in a visit.
Chitrod:
This place evoked into regular inhabitance during the separation and displacement of the people India. The name of this place reveals the great Mahatma's ashes which are immersed at Kandla Creek. Kandla is the only free trade region of the country and is situated 12 km to the southeast of Gandhidham. The other important tourist interests are Khavada, Bhardeshwar, and Purneshwar.
Kera:
This town is known to be the ancient place of Gujarat, the famous 10th century holy shrine dedicated to Lord Shiva is situated here, Kera was once the capital of the famous ruler Lakho Fulani, this ancient ruler have left back a marvelous monument during his reign, namely kapilkot fort, this is one of the tourist attraction here. Apart from this the major annual event of Urs celebrations at the shrine of Gulam Ali Shah, pulls in thousands and thousands of devotees from various spots of the country.
Lakhpat:
Today, this spot is noted to be a remote area with less inhabitants sojourn right here, perhaps! The erstwhile living was massive during the year 1851 and known to be as the important trade zone. It is said that by Rao Lakha who founded this place , therefore they name Lakhpat and also there are other reasons to define the name, such as, during the greenish days of living ,the people of Lakhpat made 1,00,000 kori a day ( an old currency of Kutch state) this spot is exactly situated at the junction of Kori Creek and Rann of Kutch on the Pakistan borders, this fortified town is noted for its high walls and gates and bastions of hard stone, of course almost everything around here is perished and looks deserted.
Mandvi:
This spot is said to be the biggest tourist location of the state, the town is famously known for its historical values dates back even before 18th centuries. This town is a port of Maharao of Kutch and it is located on the banks of Rukmavati River in the Gulf of Kutch, at the west coastal in India. The major tourist spot of visit is the Mandvi port which is known to be very ancient and trade zone of handicraft items. The docks at the beach is also a famous spot, where you watch ship building, then the ancient temple of Mulnayak devoted to Bhagawan Shantinath is also an attraction at this port. The Vijay Vilas Palace situated around 8km were once the retreat centre of Maharaos of Kutch during summer, this palace ages from 1940 and exhibits great architectural values and textures designs of great workmanship. The next best landmarks are the famous Aina mahal built in the mid -18th century by Ram Singh and the tomb of Gosh Mohammad, Gurdwara and some more Hindu based temples are the added attractions nearby. The Kalyaneshwar temple and the Narayan Sarovar situated 49 km near and Koteshwar adds an enlighten trip over here, this town of old age offers a splendid trip on sight seeing enrolls old buildings of princely times, chronological palaces and temples, apart from this the town offers valuables of silverware, shell work items, Kutch embroideries, tie- dye sarees, block prints and Bandhini- a form of cloth printing for purchase.
Mundra:
This is another coastal city of the state, and famously known as 'the Paris of Kutch' which was founded during the reign of Rao Bhojraji (1633-1645). The famous attraction here is the high fortified stone wall constructed of huge massive blocks taken from the ruins of Bhadreshwar, a holy city of Jains. The major produces of products are the handicrafts of Mundra, tie-dye, block prints and Namda works of Mansoori people are famous and awesome.
Tera:
This is a Teerth and an ancient temple situated here as the major attraction of tourist. The Tera fort known as Darbargarh is situated here as an added attraction, this place is surrounded by ancient temples, havelis, forts and lakes as tourist trips at serene… the temple of Shri Shymala Parshwanath Bhagvan and Shri Naliya Teerth are the another major tourist attractions nearby.
Narayan Sarovar:
This spot is considered to be the unique location of the country for its arid zone and uncommon ecosystem. This arid zone is a splendid space of 444 sq'km filled in with thorny jungle and great habitat of chinkara and Indian Gazelle. The other species and animals found here are caracal, ratel, wolf, desert cat, and desert fox, great Indian bustard, lesser florican, blue bull, spotted deer, wild boar and a variety of water fowls. The best season of visit is September to January.
Dholavira:
Above all the Harappan sites, the site of Dholavira nearby known as Kotada, in the Khadir island of Kutch stands separately. It is memorable for its wonderful planning and vastness of area and deposit. Currently, we can say that it is one of the two largest arrangements in India and the fourth or fifth largest in the subcontinent. The others arrangements are: Mohenjo-daro, Harappa, Gharo Bhiro (all in Pakistan) and Rakhigarhi (in India).Dholavira enjoys the exclusive characteristic of elastic a dedication of ten large sized signs of the Harappan script that is indeed the oldest sign-board of the world. A variety of used funerals structures is yet another feature of greater than importance throwing new light on the socio-religious beliefs by this means representative the presence of compound national groups in the Indus population of Dholavira.
Jakhau Port:
Jakhau Port in Kutch Jakhau Port is also one of the oldest ports of Kutch. Today, this port is only used for fisher men. Jakhau Port has its own importance. This is a very beautiful Port of Kutch. There is a centre for coastguard and water department of B.S.F. in Jakhau Port.
Kandla Port:
Kandla Port, a national port, is one of the eleven most important ports of India. This port is situated on Kandla stream. The first investigation of this stream was undertaken by the British Royal India Navy in 1851 and a detailed survey done in 1922. This port is developed by Joint project of Maharao Shree Khengarji-III and British Government in the 19th century. Standard dry cargo treatment capacity of Kandla Port is 24,000 metric tons per day.
Koteshwar:
In the district of Lakhpat is situated the temple of Koteshwar which is a holy place of pilgrimage in Kutch. There is an ancient story attached with it. They say that King Ravana wanted to be immortal and did tapasya of God Shiva. Lord Shiva gifted him with Ling which he could worship and become immortal. But in arrogance he dropped the ling, which on touching the ground turned into a thousand Lings. King Ravana could not recognize the original ling, and so the boon was lost. There were a thousand lings at that place so the Gods of heaven decided to build this temple and name it Koteshwar.
Bhadreshwar Jain Temple:
Bhadreshwar Jain Temple in Kutch There are a number of temples built by Jain followers in Kutch. The Bhadreshwar temple, one of the most ancient temples situated in Bhadrawati, considered a very holy place is one such. Bhadrawati was ruled by King Sidhsen in 449 B.C (according to the Hindu calendar) who renovated the place. Later it was ruled by The Solankies who were Jains, and they changed the name to Bhadreshwar. Then in 1315, a great famine struck Kutch, after which the place was renovated by Jagadusha.
Nearest Petrol Pump:
Reliance Petrol Pump::Bhuj,Kutch,Gujarat,India
Pragpar Petrol Pump:Kutch,Gujarat,India
IBP Petrol Pump:Gandhidham,Kutch,Gujarat,India
Hotels/Lodge/Accommodation:
Hotel Prince:College Road,Mirzapar Highway,Bhuj,Gujarat,India
Hotel Mahir: Mandvi,Kutch,Gujarat,India,ph:02834 222090
Things to carry:
Tips & Suggestions:
Help Line/Phone Number:
Police Station:100
Nearest Hospital:
Mental Hospital:Bhuj,Kutch,Gujarat,India
Velani Hospital:Bhuj, Kutch, Gujarat,India
Society/Community Phone Number:
Link:www.gujaratguideonline.com
Dynamic View
The temple will have an easy access by public transport and will serve as a permanent place of assembly for worship and Gujrati classes of Melbourne have had to use various Scout halls and School halls previously.These halls have not always been available when needed and thus a decision was made by the Mandir to search for an appropriate place that may be available to us when needed,The model of Swaminarayan temple, that will come in existence in sort time, with the hearty help of holy devotees of supreme god Swaminarayan. This mandir falls in Uttar Desh.....more
Kutch Mandvi Beach
Mandvi beach isone of the finest beach of Gujarat and a historic port town of the Maharao of Kutch. The port of Mandvi was an important sea trade post between the near East and the far East which brought prosperity to the Royal family. Mandvi town was an important city for the Maharaos of Bhuj being endowed with some splendid palaces and buildings. The region surrounding the Kutch Mandvi beach was once very active and significant, and one may come across many ruins and historical sites. Some distance away from the pristine Kutch Mandvi Beach is an ancient dock and port, which is still functional today. Though not historically significant, as the dock/port is completely recent, it is unique in that here, the vessels are made using wood and by hand....more
Prag Mahal Bhuj
The Prag Mahal in Bhuj is one of the most interesting palaces amongst the famous monuments in Gujarat India. The Prag Mahal also called the New Palace, was constructed in the year 1979. Every year tourists from far and wide come to see the splendors of this beautiful architectural structure which stands intact till date to narrate the tales from the bygone era.The Prag Mahal in Bhuj is an example of magnificent architecture. The decor of ornate Italian marble and golden sandstone give the palace a unique look and leaves one spellbound. The attractive Corinthian pillars of Prag Mahal, Bhuj and the detailed Jaali work depict the European flora and fauna. You can spend hours after hours studying and admiring the beautiful art work of Prag Mahal, one of the major tourist attractions in Gujarat....more
Aina Mahal Bhuj
Aina Mahal was constructed by Rao Lakhpatji, is situated in historic city of Bhuj, Gujarat. The mid eighteenth century Palace was built in traditional Kutchi style showing strong European influence as well. Aina Mahal is part of a large palace complex, with a darbar hall, a hall of mirrors and suites for the royal members. The Hall of Mirrors which is a blend of Indian and European creativity is the main attraction of the palace. The walls of this hall are built of white marble and are covered by mirrors surrounded by gilded decorations.The Aina Mahal in Bhuj is an old palace that was built in the 18th century. The erstwhile palace which belonged to Maharao Lakhpatji has now been transformed into a museum that is one of the chief tourist attractions in Bhuj.....more
Durbar Gadh Bhuj
Durbar Gadh is one of the most beautiful tourist attractions in Bhuj, Gujarat. The monument is located in the heart of the old town of Bhuj. It has immense historical importance. Every year, tourists flock to Durbar Gadh, Bhuj that happens to be one of the most remarkable landmarks in the city.Durbar Gadh is the place where the Maharaja of Nawanagar used to hold meetings with the public audiences. It falls under the headquarters of the Kutch District in Gujarat. This historical building was affected by the massive earthquake of 2001. Some of the distinct features of the fort are the beautiful latticed windows and intricate carvings that adorn its exteriors and interiors. A tour to Durbar Gadh in Bhuj is a must during your visit to Gujarat....more
Tomb of Jesal Toral
Anjar, which is one of the most beautiful cities in Gujarat, houses some of the most attractive forts and monuments. The Tomb of Jesal Toral is one of the famed tourist attractions in Anjar. It is basically a samadhi of Jesal Toral. There is also a bungalow of James Mcmurdo here. It has now been converted into a veritable museum that displays Kutch art.Anjar is also famed for its beautiful block printing work, scissors, nutcrackers and penknives. These are some of the artworks which you will come across in the museum at the Tomb of Jesal Toral in Anjar. On your visit to the city, a tour to Jesal Toral Tomb is highly recommended as it is one of the premier attractions of Gujarat. The tomb is also a centre for fairs.....more
Dholavira Ruins Kutch
Kutch is spelt as Kachchh also, It is a beautiful district of western state of Gujarat in India. It is said to be the most extensive district in the state of Gujarat and the 2nd largest district of India succeeding Leh. The meaning of the word Kutch stands for something that becomes wet and dry intermittently. On tour to Gujarat you must stop at this magnificent travel destination for a while. Here you will get to see various types of interesting sites of which forts and monuments top the chart. In fact Dholavira Ruins in Kutch has been acclaimed massively among all the forts and monuments in Gujarat.Dholavira is an ancient town situated in the state of Gujarat. It lies on the North West corner of the Khadir Island and stands surrounded by water in the monsoons. It was discovered in the year 1967 AD.....more
Vijay Vilas Palace Mandvi
Mandvi was earlier popular as the Paris of Kutch. This is because the Maharajas of Kutch made this place their summer resort because of its pleasant climate. With its rich traditional history a tour to Mandvi is a must on your visit to the forts and monuments in Gujarat. The Vijay Vilas Palace in Mandvi is one of the best examples of the city glamorous historical background.The Vijay Vilas Palace rises from a multi acre estate along the coast near the town. This palace of His Highness Maharao Vijay Singhji who ruled over Kutch in the 1940s is an eclectic blend of architectural styles. Umbrella domes like those seen in palaces of Bengal cupolas that would not look out of place in Mughal buildings jarokhas and cusp arches like those seen in Rajput palaces of Rajasthan, Victorian Gothic arches and classical columns make up the ensemble. Yet the architects were skilled enough to make the entire complex look harmonious....more
Tomb of Ghosh Mohammed Kaba
he tomb of Ghosh Mohammed Kaba in Lakhpat is amongst the best tourist attractions in Gujarat, India. The town of Lakhpat is at a distance of 151 km from the Bhuj airport. The town has an amazing landscape. It is also known for its rich historical splendors, which you can see in the form of old temples, gurudwaras and mosques. The tomb of Ghosh Mohammed Kaba is very famous and attracts a lot of tourists.From the vantage point on the wall of the tomb, a breathtaking view of the sea and the Rann of Kutch can be enjoyed. The town of Lakhpat is now deserted and uninhabited. Amongst the ruins of the town, the one that stands prominent is the Gurudwara or the holy shrine of the Sikhs. The tomb of Ghosh Mohammed Kaba is about 200 years old. It is a gigantic tomb that still stands to narrate stories from the bygone era....more
Kutch Museums
Kutch Museum, formerly known as the Fergusson Museum, is situated in the ancient city of Bhuj, in Kutch , it is the oldest of its kind in Gujarat. The museum, constructed in the Italian Gothic style, is located in the picturesque surroundings on the bank of Hamirsar Lake just opposite to the Nazar Bagh Garden.The Kachchh Museum in Bhuj, India, is one of the famous Tourist Attractions in Bhuj. Built during the period of British Rule in India, the Museum of Kachchh in Bhuj is the most significant among all other Museums in Bhuj as it displays the articles that take the visitors to those ages to which they belonged....more
Folk Museum Bhuj
The Folk Museum in Bhuj, India, is also known as Bharatiya Sanskruti Darshan, Bhuj.This museum has an interesting collection of artifacts including textiles which are displayed at typical village habitat. The Bhuj area has tribal people namely the Rabaries,Jats and Ahir to name a few. Therefore the museum here is rich in folk culture and art and is a must see.One of the chief attractions of Folk Museum, Bhuj which you will hardly find in any of the other Museums in Bhuj, is a rare fossil of a Crocodilian which is which is an extinct species of the crocodile of the modern age. This creature was double the size of a crocodile of today measuring as much as 9 meters as compared to the modern species which measures only 3 to 4 meters in length.Apart from this, a wide range of textiles and artifacts belonging to the members of the royal families of Bhuj have been elaborately displayed in Folk Museum, Bhuj. These timeless items have become hallmark of the glorious past when Bhuj was under the rule of the Rajputs. The private collections of the rulers arouse interest and amazement among visitors of all ages. The Museum also houses models of villages of this part of the world....more
Narayan Sarovar Sancuary
Located about only 2 kms away from the Kutch district in Gujarat, the Narayan Sarovar Chinkara Sanctuary is considered as one of the most unique wildlife sanctuaries in India. The sanctuary is also known as the Narayan Sarovar Wildlife Sanctuary and is mainly dedicated at preserving and conserving the endangered species of Chinkara or the Indian Gazelle. The sanctuary was established in April, 1981 and has been holding a special place among the nature lovers all over the world, since then.It covers a huge area of 444 sq. km.The Narayan Sarovar Chinkara Sanctuary has a unique eco-system. A part of the sanctuary is a seasonal wetland in the arid zone that play mother to 15 threatened wildlife species.....more
Kutch Bustard Sanctuary
The Kutch Bustard Sanctuary is one of the great wonders of wildlife in Gujarat. With amazing geographical features, flora and fauna, the sanctuary simply leaves you spellbound with its wild splendors. Spread over an area of 2 sq km, Kutch Bustard Sanctuary is located in proximity to Naliya which is under the district of Kutch in Gujarat India. The sanctuary was established with an aim to protect the great Indian Bustard.The total population of the species of Indian Bustards has reduced considerably since the last few years due to various reasons like poaching, hunting and others.....more
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Enbridge Announces Adoption of Advance Notice Bylaw
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Enbridge Inc. to Webcast 2015 Guidance Conference Call
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Active anodes were fabricated via wet chemical impregnation of optimized amount of La0.4Sr0.6TiO3 (L4ST) into La0.4Ce0.6O1.8 (LDC) pre-infiltrated porous yttria-stabilized zirconia (YSZ) matrix. Impregnations of 10 wt% LDC with 16 wt% L4ST significantly improved the performance of the fuel cell from 48 mW cm−2 for pure L4ST to 161 mW cm−2 for LDC–L4ST at 900 °C in H2. The contribution of the pre-loaded LDC to this improvement was investigated using electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM) as well as transmission electron microscopy (TEM). The measurement results indicated that pre-infiltrated LDC increased the activity of the anode more effectively by decreasing the total polarization resistance of the cell from 3.3 Ω cm2 to 1.0 Ω cm2 in humidified H2 at 900 °C. More importantly, the LDC nano-deposits (<20 nm) behaved as an effective "adhesive" that substantially enhanced the wettability of L4ST on YSZ matrix, resulting in finer and more uniform structure of L4ST infiltrates. The LDC–L4ST cells also demonstrated significantly improved performances in 0.5% H2S–H2 and 0.5% H2S–CH4 with higher stability than cells with pure L4ST anode.


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HomeTech UpdatesGeneral NewsPhil Weiser wins the Democratic nomination for Colorado attorney general after Joe Salazar concedes
Jul. 01, 2018 at 5:56 am
Phil Weiser wins the Democratic nomination for Colorado attorney general after Joe Salazar concedes
Geneva A. Crawford 2 years ago January 28, 2019 attorney generalcolorado attorneydewey changeddewey turnedgordon turnedjoe salazarphil weiserspecial prosecutoryork city
Phil Weiser, a former dean of the University of Colorado Law School, has received the Democratic number one for Colorado attorney trendy over kingdom Rep. Joe Salazar.
Salazar conceded Saturday after the ultra-modern vote totals from the Colorado Secretary of State's workplace confirmed him extra than 5,000 votes at the back of Weiser. The victory, which comes 4 days after Election Day, is a beautiful win for Weiser, for the reason that he had a mountain to climb over Salazar's enormous name reputation.
"I am humbled and commemorated by this win. I had a brilliant name with Joe Salazar earlier today, and we are excited to work collectively to make certain Colorado has a Democratic Attorney General in 2018," Weiser stated in an announcement Saturday. "Joe is a fierce suggest for social justice and a true fighter for the ones much less fortunate, from the homeless to the ones handled unfairly via our criminal justice device. I am a far better candidate because of the enjoy jogging towards him on this number one and share his commitment to being attentive to individuals who aren't frequently heard."
Weiser, who also worked for former President Barack Obama, turned into planning to spend extra than $500,000 in the weeks main up to primary Election Day on television ads seeking to get his name and message out before voters. Those efforts had been boosted by using an overdue endorsement from Gov. John Hickenlooper — the Democrat's most effective endorsement of a statewide candidate in a primary contest.
Salazar, alternatively, won backing from Vermont U.S. Sen. And former presidential candidate Bernie Sanders, running an anti-status quo marketing campaign with guarantees of shaking up the Colorado Attorney General's Office.
"I need to in reality congratulate our nominee, Phil Weiser," Salazar stated in an assertion Saturday conceding the race. "He ran a first-rate campaign in a hard race. We've begun a number of conversations approximately the importance of the Attorney General's workplace, the way to make certain fairness and justice are priorities of our elected officials, and approximately the destiny of the Democratic birthday party.
JUNE 29, 2018 Ahead of high-stakes midterms, Barack Obama plans a bigger position in political races
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JUNE 27, 2018 Joe Salazar isn't backing down in the Democratic primary for Colorado lawyer widespread, no matter Phil Weiser's lead
The three-term lawmaker was boasting in recent months approximately keeping a double-digit lead inside the polls over Weiser, whom he painted as unqualified and out of contact with Colorado's hobbies.
But Salazar trailed Weiser in fundraising, to the track of extra than $1 million, and didn't get the identical form of backing from the country's large-name Democrats as Weiser had.
Weiser will face 18th Judicial District Attorney George Brauchler, the GOP nominee, in November.
Republican Cynthia Coffman, the state's cutting-edge lawyer widespread, is leaving workplace after one time period. She made a failed bid to be Colorado's subsequent governor.
Dewey, Thomas E. – Special Prosecutor From Hell
He changed into a median-spirited runt; a bit man with a huge mustache that appeared to dominate his snarling face. But liberal Republican Thomas E. Dewey, a man who made his bones as a Special Prosecutor in New York City and who might prevent at not anything to in addition his skyrocketing career, turned into simply an eyelash far from becoming the President of the USA.
Dewey changed into born on March 24, 1902, in the little metropolis of Owosso, Michigan. Dewey's father became the editor and writer of the nearby newspaper — the Owosso Times. Dewey senior's challenge in life turned into to right the wrongs of the political global, especially the tyranny of Tammany Hall, a corrupt Democratic political gadget, based in New York City, but with tentacles all around America. Dewey Jr. Favorite his father's zeal and it becomes this that later inspired Dewey to go after prepared crime figures in New York City, with a vengeance that not usually adhered to the letter of the regulation.
But first Dewey desired to sing.
Dewey was a talented operatic baritone, and at the same time as he turned into attending the University of Michigan he joined the Phi Mu Alpha Sinfonia, a countrywide fraternity for guys of a track. Dewey turned into also a member of the University of Michigan Men's Glee Club. Following in his father's footsteps, Dewey wrote for The Michigan Daily, the university's scholar newspaper. However, Dewey turned into higher at making a song that he turned into at writing, a lot so, in 1923, Dewey completed 0.33 inside the National Singing Contest. However, Dewey soon evolved throat problems, and despite the fact that he in short considered a career in track, he modified his mind and opted to be a legal professional rather.
With his father's money, Dewey traveled to New York City and enrolled on the Columbia Law School. One of his classmates changed into the novel socialist/communist Paul Robeson, who has become a singer and actor of some be aware, in among transferring to and from the USA he simply cherished – Russia. However, Dewey changed into no idealist like Robeson. After he graduated regulation college in only years, Dewey decided to grasp up his own shingle and move into personal practice, which he did from 1925-31. In 1928, Dewey married actress Frances Hutt. After their marriage, Dewey's wife ceases acting, and they sooner or later raised sons: Thomas E. Dewey, Jr., and John Martin Dewey. attorney general after Joe Salazar concedes" />
In 1931, Dewey turned into named leader assistant to George Medalie and turned into given the reputable title of Chief Assistant U.S. Attorney for the Southern District of New York. This became the springboard Dewey had to further a political carer that knew no barriers and counted heavily on felony improprieties.
In 1933, Dewey first important case turned into the prosecution of former pickpocket Irving Wexler, better called Waxey Gordon. Gordon turned into a protégé of Arnold Rothstein, taken into consideration "The Godfather" of the modern gangster. In 1928, after Rothstein changed into killed over a massive playing debt, Gordon took over all of Rothstein's operations — in the bootlegging, and in the playing commercial enterprise. Gordon's companions in crime blanketed such illustrious gangsters like Lucky Luciano, Louis "Lepke" Buchalter, Gurrah Shapiro, and Meyer Lansky. Even after slicing in his partners, Gordon turned into said to have revamped $2 million a year in profits.
However, Gordon and Lansky hated every different, and after Dewey unsuccessfully tried to prosecute Gordon for his crimes, Lansky, with the blessing of Luciano and Buchalter, funneled facts, consisting of documentation to Dewey that confirmed that perhaps Gordon turned into now not paying his fair proportion of this earnings taxes. Using the equal tactic the government had used in opposition to Al Capone, Dewey, now inside the possession of books that stated Gordon had hidden $5 million in taxable earnings over a ten-yr duration, decreased the hammer on Gordon. He pass-examined Gordon with such cruelty, spit became proverbially flying from Dewey's mouth and down his copious mustache. Gordon, basically an oaf with the mentally and vocabulary of a ten-year-old, was no fit for Dewey at the witness stand. After the most one-facet trial that would probably occur, Gordon becomes slapped with a 10-12 months prison sentence.
Dewey subsequent set his attractions on Dutch Schultz.
By the time Dewey changed into ready to prosecute Schultz, it was alleged that District Attorney William C. Dodge become now not aggressively going after the mob and crooked politicians, and there had been plenty of both in New York City. In 1935, Dewey was given a bump up in rank, when Governor Herbert H. Lehman, bypassing Dodge, appointed Dewey as Special Prosecutor in New York County (Manhattan). With the backing of Governor Lehman, Dewey assembled a crack team of workers of greater than 60 assistants, investigators, manner servers, stenographers, and clerks. New York Mayor Fiorello H. La Guardia chipped in with 63 of his pleasant law enforcement officials to the purpose, and Dewey becomes on the pinnacle of the prosecutorial global.
Dutch Schultz, born Arthur Flegenheimer on August 6, 1902, become the most seen mobster in New York City, however he became most effective one of the nine-member National Crime Commission, that covered Italians gangsters Lucky Luciano and Frank Costello, as well as fellow Jewish contributors Meyer Lansky, Bugsy Siegel, and Louis "Lepke" Buchalter. During Prohibition, Schultz made tens of millions inside the sale of unlawful beer, and was nicknamed "The Beer Baron of the Bronx." In the early 1920's, Schultz bulldozed his way into the Harlem numbers rackets, pushing apart remarkable black number kings Madame Stephanie St. Clair, Bumpy Johnson, and Casper Holstein. Noted crime writer and former cop Ralph Salerno as soon as stated, "Schultz asked the black numbers to a meeting in his office. When they got here in, Schultz put his 40-five on the desk and said, "I'm your associate.'"
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Juan Brouwer and his bet with digital art
Juan Brouwer (1973) did not choose the path of art that friends and family expected, being the son of an outstanding Cuban musician and composer. Although he dabbled in music and studied saxophone very quickly, he became convinced that he had not inherited the melodic abilities of his father and that in music matters he preferred to be a spectator.
The gift of some acrylic paintings and the invitation to visit galleries made him discover the world of plastic arts and take it as a means of expression and way of life. "From my first approach to painting, abstractionism as a style monopolized all my interest."
Large formats, reduced color palettes where warm tones and complementary contrasts take center stage, visual and tactile textures, associations with past works without being unconscious repetitions, are hallmarks that distinguish Juan Brouwer's pictorial work. "At present my creative process does not a priori contain an external reference, a fact that in my opinion is closer to pure abstraction; it is about painting by and from painting ".
"The act of painting provokes in me a kind of trance - he confesses - where only the laws of composition and color intervene, a journey to the sense of the interior. It is at this moment where I feel the freedom and spiritual peace, which leads me to the final result, from chance and containment the final work spontaneously forms before my eyes ".
According to the artist, in this process of creation, the abstract is transcendent, since it acts as a catalyst for emotions in a complex and dizzying world, where human beings are saturated with images. For this reason, he does not propose to offer the public lines of interpretation "polysemy is richer," he says.
As a constant student of plastic arts Juan Brouwer recognizes the importance of revisiting the exponents of abstractionism and being attentive to the new ways of doing that are handled in the world, "after 100 years of this manifestation, only those who know how to innovate from already done ".
With this premise, he recently ventured into digital art (NFTs), a novel alternative that broadens the horizons of visual arts. In his proposals his painting and his music come together harmoniously, like a kind of collage, giving the public a sensory spectacle.
"In these clips, which are about a minute long, what I try to do is play with the colors and textures of the main work, duplicate the frames, overlap one another and change their tones. The NFTs could be the end result of the work if I was willing to continue working on it ".
Freedom of creation is a characteristic that abstractionism shares with Jazz, that is why the artist relies on this musical genre to consolidate the message. The melody of the flamenco cajon, played by the virtuoso Cuban musician Ruy Adrián López-Nussa, together with the versatile textures and colors, invite the viewer to action, abandon all inactive and face new paths.
Juan Brouwer declares that his foray into this medium is instinctive, since he knows little about the system in which it develops, however his early works have been liked by critics, contemporaries and the public, an effect that motivates him to continue experimenting. "The world is heading into the digital age at a dizzying pace, and I believe that NFTs offer endless creative possibilities," he says.
In a scenario where any user is capable of creating audiovisual content and archiving it under the title of digital art, where postmodernity has blurred all limits, where commodification prevails over talent and sacrifice, Juan Brouwer's NFTs are like a fresh breeze leaving see that there are still hands committed to the good work of the visual arts.
By Naimy Herrera, November 2021