Polynomial constants of motion in flat space

DOI10.1063/1.526114zbMath0549.70008OpenAlexW2019991066MaRDI QIDQ3341965

Gerard Thompson

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1063/1.526114

zbMATH Keywords

Killing tensorcommuting integrals for a Hamiltonian systempolynomial in the momenta

Mathematics Subject Classification ID

Hamilton's equations (70H05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (21)

Cubic first integrals of autonomous dynamical systems in E2 by an algorithmic approach ⋮ On superintegrable systems separable in Cartesian coordinates ⋮ Conserved vectors for the autonomous system \(\ddot r+g(r,\theta)\hat r+h(r,\theta){\hat \theta}=0\) ⋮ Integrable 2D time-irreversible systems with a cubic second integral ⋮ Second-order systems with Runge-Lenz-type vectors ⋮ Comment on an aspect of a paper by G. Thompson ⋮ Killing tensors in spaces of constant curvature ⋮ Lie group symmetries and invariants of the Hénon–Heiles equations ⋮ Structural equations for Killing tensors of arbitrary rank ⋮ Doubly exotic \(N\)th-order superintegrable classical systems separating in Cartesian coordinates ⋮ One-dimensional nonautonomous dynamical systems with exact transcendental invariants ⋮ Lax formalism for a family of integrable Toda-related n-particle systems ⋮ Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach ⋮ Quadratic first integrals of autonomous conservative dynamical systems ⋮ Higher order first integrals of autonomous dynamical systems ⋮ A unified treatment of cubic invariants at fixed and arbitrary energy ⋮ Degenerate integrable systems on the plane with a cubic integral of motion ⋮ On two-dimensional integrable models with a cubic or quartic integral of motion ⋮ Symmetries, separability and volume forms ⋮ Generalisations of the LaplaceRungeLenz Vector ⋮ Superintegrability of the caged anisotropic oscillator

Cites Work

• Three integrable Hamiltonian systems connected with isospectral deformations
• Killing tensors and the separation of the Hamilton-Jacobi equation
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Killing Tensors and Variable Separation for Hamilton-Jacobi and Helmholtz Equations
• A further note on the Hénon–Heiles problem

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