New integrable problem of classical mechanics

DOI10.1007/BF01209304zbMath0576.70004WikidataQ125898472 ScholiaQ125898472MaRDI QIDQ1064795

Oleg I. Bogoyavlenskij

Publication date: 1984

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

zbMATH Keywords

quadratic potentialPrym varietyintegrable problemLiouville's integrability theoremNewtonian fieldRiemann theta-function

Mathematics Subject Classification ID

Free motion of a rigid body (70E15)

Related Items (11)

Integrable cases of a rigid body dynamics and integrable systems on the ellipsoids ⋮ A new integrable case of the motion of the 4-dimensional rigid body ⋮ Poisson variations in the problem of the stability of equilibria in rigid body mechanics ⋮ Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability ⋮ Equivalent problems in rigid body dynamics ? I ⋮ Kowalewski top and complex Lie algebras ⋮ Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi-Mumford systems ⋮ Hamiltonian structure, equilibria, and stability for an axisymmetric gyrostat motion in the presence of gravity and magnetic fields ⋮ General integrable problems of classical mechanics ⋮ On the stability of motion of a gyrostat about a fixed point under the action of non-symmetric fields ⋮ Euler equations on finite dimensional Lie algebras arising in physical problems

Cites Work

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• Geodesic flow on \(SO(4)\) and Abelian surfaces
• Linearization of Hamiltonian systems, Jacobi varieties and representation theory
• Completely integrable systems, Euclidean Lie algebras, and curves
• Some remarks on the integrability of the equations of motion of a rigid body in an ideal fluid
• E-compact extensions of topological spaces
• Theta functions and non-linear equations

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