INTEGRABLE CASES OF THE DYNAMICS OF A RIGID BODY, AND INTEGRABLE SYSTEMS ON THE SPHERESSn

DOI10.1070/IM1986v027n02ABEH001174zbMath0616.70008OpenAlexW2156319131MaRDI QIDQ4725793

Oleg I. Bogoyavlenskij

Publication date: 1986

Published in: Mathematics of the USSR-Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im1986v027n02abeh001174

zbMATH Keywords

Lagrangian systemsRiemann theta functionsintegrable rigid body dynamicscentral force fieldequations of rotationmagnetic momentsdistribution of electric chargesLie groups homomorphismsinfinite-dimensional set of solutionsspherically symmetric inertia tensor

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Free motion of a rigid body (70E15) Applications of Lie groups to the sciences; explicit representations (22E70) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Lagrange's equations (70H03) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (5)

Regular precession of a rigid body (gyrostat) acted upon by an irreducible combination of three classical fields ⋮ One family of conformally Hamiltonian systems ⋮ On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies. ⋮ Bäcklund transformations relating different Hamilton-Jacobi equations ⋮ On the Chaplygin system on the sphere with velocity dependent potential

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