Integrable Hamiltonian systems with vector potentials

Pucacco G., Rosquist K.

We investigate integrable two-dimensional Hamiltonian systems with scalar andvector potentials, admitting second invariants which are linear or quadratic in themomenta. In the case of a linear second invariant, we provide some examples ofweakly integrable systems. In the case of a quadratic second invariant, we recoverthe classical strongly integrable systems in Cartesian and polar coordinates andprovide some new examples of integrable systems in parabolic and ellipticalcoordinates