sentences:  Fiber derivative
  
  In the context of Lagrangian Mechanics the fiber derivative is used to convert between the Lagrangian and Hamiltonian forms.In particular, if formula_1 is the configuration manifold then the Lagrangian formula_2 is defined on the tangent bundle formula_3 and the Hamiltonian is defined on the cotangent bundle formula_4—the fiber derivative is a map formula_5 such that
  
  where formula_7 and formula_8 are vectors from the same tangent space.