Euler equations on finite dimensional Lie algebras arising in physical problems

DOI10.1007/BF01212401zbMath0581.58022MaRDI QIDQ1067670

Oleg I. Bogoyavlenskij

Publication date: 1984

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

zbMATH Keywords

integrabilityEuler equationsLie algebrasrotation of a magnetized rigid body

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (17)

NEW ASPECTS ON THE GEOMETRY AND DYNAMICS OF QUADRATIC HAMILTONIAN SYSTEMS ON (𝔰𝔬(3))* ⋮ Lax representation with a spectral parameter for the Kowalevski top and its generalizations ⋮ Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields ⋮ Explicit determination of certain periodic motions of a generalized two-field gyrostat ⋮ Regular precession of a gyrostat in three uniform fields ⋮ Topological atlas of the Kovalevskaya top in a double field ⋮ On a class of three-dimensional quadratic Hamiltonian systems ⋮ Separation of variables in the generalized 4th Appelrot class ⋮ Phase topology of one system with separated variables and singularities of the symplectic structure ⋮ The free rigid body dynamics: Generalized versus classic ⋮ The Kowalewski top: A new Lax representation ⋮ Hamiltonian structure, equilibria, and stability for an axisymmetric gyrostat motion in the presence of gravity and magnetic fields ⋮ Extensions of the Appelrot classes for the generalized gyrostat in a double force field ⋮ The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions ⋮ Discriminantly separable polynomials and the generalized Kowalevski top ⋮ LIE–HAMILTON SYSTEMS: THEORY AND APPLICATIONS ⋮ On the stability of motion of a gyrostat about a fixed point under the action of non-symmetric fields

Cites Work

• Models of Gross-Neveu type are quantization of a classical mechanics with nonlinear phase space
• Integrable Euler equations on SO(4) and their physical applications
• New integrable problem of classical mechanics
• Lax representation for the systems of S. Kovalevskaya type
• Magnetohydrodynamical model of pulsar rotation. Exact periodic solutions

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