Canonical transformations of the extended phase space, Toda lattices and the Stäckel family of integrable systems

DOI10.1088/0305-4470/33/22/318zbMath0989.37075arXivsolv-int/9909006OpenAlexW2007878853MaRDI QIDQ4507726

Publication date: 8 October 2000

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

Full work available at URL: https://arxiv.org/abs/solv-int/9909006

zbMATH Keywords

Toda lattices completely integrable system Kepler transformation Maupertuis-Jacobi mappings

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton-Jacobi equations in mechanics (70H20) Lattice dynamics; integrable lattice equations (37K60) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (11)

On Reciprocal Equivalence of Stäckel Systems ⋮ Killing tensors with nonvanishing Haantjes torsion and integrable systems ⋮ Modeling and passivity analysis of nonholonomic Hamiltonian systems with rheonomous affine constraints ⋮ Transformation of the Stäckel matrices preserving superintegrability ⋮ The Maupertuis Principle and Canonical Transformations of the Extended Phase Space ⋮ Change of the time for the periodic Toda lattices and natural systems on the plane with higher order integrals of motion ⋮ One invariant measure and different Poisson brackets for two non-holonomic systems ⋮ Degenerate integrable systems on the plane with a cubic integral of motion ⋮ Hamiltonization and separation of variables for a Chaplygin ball on a rotating plane ⋮ Third-order superintegrable systems separable in parabolic coordinates ⋮ Unconfused ultraconservative multiclass algorithms

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