Integrable Hamiltonian systems with vector potentials

Abstract

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.

23 pages, Submitted to Journal of Mathematical Physics

References in corpus (2)

• Integrable and superintegrable quantum systems in a magnetic field
• Invariants at fixed and arbitrary energy. A unified geometric approach

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