Relations between integrable systems in plane and curved spaces

DOI10.1007/s10569-007-9098-1zbMath1202.70062OpenAlexW1965542242MaRDI QIDQ2465018

Alexey V. Borisov, Ivan. S. Mamaev

Publication date: 19 December 2007

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-007-9098-1

zbMATH Keywords

Integrable systemsEuclidean spaces

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Celestial mechanics (70F15)

Related Items (14)

Sundman transformation and alternative tangent structures ⋮ An integrable Hénon–Heiles system on the sphere and the hyperbolic plane ⋮ Darboux inversions of the Kepler problem ⋮ Killing tensors with nonvanishing Haantjes torsion and integrable systems ⋮ Orbits in the problem of two fixed centers on the sphere ⋮ Projective dynamics and classical gravitation ⋮ New integrable two-centre problem on sphere in Dirac magnetic field ⋮ Projective dynamics and first integrals ⋮ On the motion of a solid body on spherical surfaces ⋮ Superintegrable generalizations of the Kepler and Hook problems ⋮ Computing hyperbolic choreographies ⋮ The spatial problem of 2 bodies on a sphere. Reduction and stochasticity ⋮ On the Equivalence Between Type I Liouville Dynamical Systems in the Plane and the Sphere ⋮ Figures of equilibrium of an inhomogeneous self-gravitating fluid

Cites Work

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• The Lagrange and two-center problems in the Lobachevsky space
• Topological analysis of the two-centre problem on the two-dimensional sphere
• Generalizing the classical fixed-centres problem in a non-Hamiltonian way
• Separabilty in HamiltonJacobi Sense in Two Degrees of Freedom and the Appell Hypergeometric Functions
• A Note on the One-Electron States of Diatomic Molecules

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