  We show the well-posed variational principle in constraint systems. In a
naive procedure of the variational principle with constraints, the proper
number of boundary conditions does not match with that of physical degrees of
freedom dynamical variables, which implies that, even in theories with up to
first order derivatives, the minimal (or extremal) of the action with the
boundary terms is not a solution of equation of motion in the Dirac procedure
of constrained systems. We propose specific and concrete steps to solve this
problem. These steps utilize the Hamilton formalism, which allows us to
separate the physical degrees of freedom from the constraints. It reveals the
physical degrees of freedom which is necessary to be fixed on boundaries, and
also enables us to specify the variables to be fixed and the surface terms.

High Energy Physics - Theory;General Relativity and Quantum Cosmology