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Lepagean 2-forms in higher order Hamiltonian mechanics. II: Inverse problem. (English) Zbl 0651.58010
Summary: The theory of Lepagean 2-forms is used to formulate and investigate the inverse problem in higher order Hamiltonian mechanics. Necessary and sufficient conditions for a system of first order ordinary differential equations to coincide with a system of equations for Hamilton extremals related with a system of (higher order) variational equations are found. The geometrical interpretation of the equations for Hamilton extremals in terms of a distribution is proposed and the relation of the Hamiltonian inverse problem to the problem of “variational integrating factors” is studied.

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
70H05 Hamilton’s equations
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