We investigate integrable two-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. (C) 2005 American Institute of Physics.
Pucacco, G., Rosquist, K. (2005). Integrable Hamiltonian systems with vector potentials. JOURNAL OF MATHEMATICAL PHYSICS, 46(1), 2701-2725 [10.1063/1.1818721].
Integrable Hamiltonian systems with vector potentials
PUCACCO, GIUSEPPE;
2005-01-01
Abstract
We investigate integrable two-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. (C) 2005 American Institute of Physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.