On Integrable Hamiltonians with Velocity Dependent Potentials |
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| Authors: | Giuseppe Pucacco |
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| Institution: | (1) Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica1, Rome, I-00133, Italy;(2) INFN – Sezione di Roma II, Rome, Italy |
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| Abstract: | We study strongly and weakly integrable 2-dimensional Hamiltonian systems with velocity dependent potentials. We determine
the set of conditions which must be satisfied in order to allow the existence of an independent second invariant polynomial
in the momenta. We then investigate the linear case for which a complete solution of the problem can be obtained. We recover
the classical set of linear strongly integrable systems and provide several new examples of weakly integrable systems whose
equations of motion can be explicitly solved at a fixed value of the energy. |
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| Keywords: | integrability of Hamiltonian systems |
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