Extension of Giacomini’s results concerning invariants for one-dimensional time-dependent potentials

DOI10.1063/1.531719zbMath0864.70010OpenAlexW271834124MaRDI QIDQ4716466

S. Bouquet, H. Ralph Lewis

Publication date: 1996

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

Full work available at URL: https://doi.org/10.1063/1.531719

zbMATH Keywords

Hamiltonian systemsinvariantmomentumnon-autonomousGiacomini's equations

Mathematics Subject Classification ID

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Kinematics (70B99)

Cites Work

• Invariants for time-dependent potentials: Use of self-similar techniques
• Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory
• Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Two- and three-resonance cases
• Invariants of particle motion in one-dimensional time-dependent potentials
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• Generalizations of Noether’s Theorem in Classical Mechanics
• Representations of one-dimensional Hamiltonians in terms of their invariants
• One-dimensional nonautonomous dynamical systems with exact transcendental invariants
• Invariant variation problems
• A second invariant for one-degree-of-freedom, time-dependent Hamiltonians given a first invariant