In the context of Lagrangian mechanics, the fiber derivative is used to convert between the Lagrangian and Hamiltonian forms. In particular, if Q is the configuration manifold then the Lagrangian L is defined on the tangent bundle T Q , and the Hamiltonian is defined on the cotangent bundle T ∗ ∗ Q —the fiber derivative is a map F L : T Q → → T ∗ ∗ Q such that