12. Hamilton-Pontryagin formulation

Since the Euler equations of the calculus of variations are identical to the Lagrange equations of analytical mechanics, it is immediately obvious that we can substitute equations analogous to Hamilton's equations. Recall that the Hamiltonian of mechanics for a system with n parameters q _i , and where conjugate variables are denoted by p _i , is a function :

H = H (p _i , q _i )

Hamilton's equations are then, in the general case : ${q^{'}}_{i} = \frac{\partial H}{\partial p_{i}}$

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