Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Two- and three-resonance cases

DOI10.1063/1.527610zbMath0626.70016OpenAlexW2058599731MaRDI QIDQ3030292

H. Ralph Lewis, João Goedert

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527610

zbMATH Keywords

driven linear oscillatorone-dimensional system with time-dependent Hamiltonianthree-resonancetwo-resonance

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Hamilton's equations (70H05) Ionized gas flow in electromagnetic fields; plasmic flow (76X05) Free motions in linear vibration theory (70J30)

Related Items (5)

Exact invariants in resonance form for time-dependent potentials ⋮ The Liouville theorem and accurate plasma simulation ⋮ Representations of one-dimensional Hamiltonians in terms of their invariants ⋮ Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory ⋮ Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials

Cites Work

• A resonance formulation for invariants of particle motion in a one- dimensional time-dependent potential
• Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• First integrals for some nonlinear time-dependent Hamiltonian systems
• Classification scheme for two-dimensional Ermakov-type systems and generalizations

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