Integrable Hamiltonian systems with velocity-dependent potentials
- 1 December 1985
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 26 (12) , 3070-3079
- https://doi.org/10.1063/1.526685
Abstract
The integrability of a two-dimensional Hamiltonian in which the potential depends explicitly on the momenta is investigated. Hamiltonians of this kind are encountered in the description of the motion of a particle in a magnetic field. Two integrable classes of potentials are identified and the second integral of motion is constructed for each of them. The singularity analysis of the equations of motion is also performed, confirming once more the relation between the (weak) Painlevé property and integrability.Keywords
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