Euler–Lagrange equations; Hamiltonian systems; Hamilton extremals; Dedecker–Hamilton extremals; Hamilton equations; Lepagean equivalents
The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.
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