Integrable Hamiltonian systems with vector potentials

Details Integrable Hamiltonian systems with vector potentials Integrable Hamiltonian systems with vector potentials

2004-05-28

arxiv.org/abs/nlin/0405065v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

23 pages, Submitted to Journal of Mathematical Physics

Scientific paper

10.1063/1.1818721

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of weakly-integrable systems. In the case of a quadratic second invariant, we recover the classical strongly-integrable systems in Cartesian and polar coordinates and provide some new examples of integrable systems in parabolic and elliptical coordinates.

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