Symmetries and conservation laws for generalized hamiltonian systems |
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Authors: | F Cantrijn W Sarlet |
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Institution: | (1) Instituut voor Theoretische Mechanica, Rijksuniversiteit Gent, Krijgslaan 271-S9, B-9000 Gent, Belgium;(2) Aangesteld Navorser bij het Nationaal Fonds voor Wetenschappelijk Onderzoek, Belgium |
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Abstract: | A class of dynamical systems which locally correspond to a general first-order system of Euler-Lagrange equations is studied on a contact manifold. These systems, called self-adjoint, can be regarded as generalizations of (time-dependent) Hamiltonian systems. It is shown that each one-parameter family of symmetries of the underlying contact form defines a parameter-dependent constant of the motion and vice versa. Next, an extension of the classical concept of canonical transformations is introduced. One-parameter families of canonical transformations are studied and shown to be generated as solutions of a self-adjoint system. Some of the results are illustrated on the Emden equation. |
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