The Euler-Poinsot top: a non-commutatively integrable system without global action-angle coordinates

DOI10.1007/BF00920045zbMath0895.70005OpenAlexW2161574934MaRDI QIDQ1366334

Francesco Fassoò

Publication date: 21 September 1998

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00920045

zbMATH Keywords

fiber bundleglobal geometric descriptionPoisson's structuretorque-free rigid body with fixed point

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Motion of a rigid body with a fixed point (70E17)

Related Items (8)

The degenerate C. Neumann system. I: Symmetry reduction and convexity ⋮ Superintegrable Hamiltonian systems: Geometry and perturbations ⋮ Long term stability of proper rotations of the perturbed Euler rigid body ⋮ COMPLETELY AND PARTIALLY INTEGRABLE HAMILTONIAN SYSTEMS IN THE NONCOMPACT CASE ⋮ Andoyer's variables and phases in the free rigid body ⋮ Compatibility of symplectic structures adapted to noncommutatively integrable systems ⋮ Perturbations of superintegrable systems ⋮ Geometric structure of ``broadly integrable Hamiltonian systems

Cites Work

• The local structure of Poisson manifolds
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Le problème général des variables actions-angles. (The general problem of action-angle variables)
• The Lissajous transformation. I: Basics
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• Manifolds, tensor analysis, and applications.
• Generalized Liouville method of integration of Hamiltonian systems
• Hamiltonian perturbation theory on a manifold
• The critical inclination in artificial satellite theory
• Examples for obstructions to action-angle coordinates
• Fast rotations of the rigid body: a study by Hamiltonian perturbation theory. Part I
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Regularization of kepler's problem and the averaging method on a manifold
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