Two-dimensional time-dependent Hamiltonian systems with an exact invariant
- 1 July 1984
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 25 (7) , 2194-2199
- https://doi.org/10.1063/1.526410
Abstract
We present a direct approach to investigate the existence of an exact invariant for two-dimensional Hamiltonians, in which the potential depends explicitly on time. The method is based on an expansion of the invariant in the velocities. The problem is solved completely for invariants linear and quadratic in the momenta. Our results contain as a particular case the results of Lewis and Leach on one-dimensional systems.Keywords
This publication has 23 references indexed in Scilit:
- A generalization of the nonlinear superposition idea for Ermakov systemsPhysics Letters A, 1982
- Comment on a letter of P. ChattopadhyayPhysics Letters A, 1981
- New nonlinear dynamical systems possessing invariantsPhysics Letters A, 1981
- Further generalization of Ray-Reid systemsPhysics Letters A, 1981
- Generalized Ray-Reid systemsPhysics Letters A, 1980
- Nonlinear superposition law for generalized Ermakov systemsPhysics Letters A, 1980
- Exact time-dependent invariants for n -dimensional systemsPhysics Letters A, 1979
- More exact invariants for the time-dependent harmonic oscillatorPhysics Letters A, 1979
- Class of Exact Invariants for Classical and Quantum Time-Dependent Harmonic OscillatorsJournal of Mathematical Physics, 1968
- Asymptotic Theory of Hamiltonian and other Systems with all Solutions Nearly PeriodicJournal of Mathematical Physics, 1962