Integrable quadratic classical Hamiltonians onso(4) andso(3, 1)

DOI10.1088/0305-4470/39/8/009zbMath1087.37047arXivnlin/0405066OpenAlexW2106645734MaRDI QIDQ3379358

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Publication date: 6 April 2006

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0405066

zbMATH Keywords

Poisson bracketPoincaré modelCasimir functionsKirchhoff modelEuler-Poinsot modelinterable Hamiltoniansmotion of a rigid body around a fixed-pointthe motion of a rigid body in ideal fluidtwo-spin interactions

Mathematics Subject Classification ID

Dynamical systems in solid mechanics (37N15) Incompressible viscous fluids (76D99) Hamilton's equations (70H05) 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) 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 (11)

Compatible Lie-Poisson brackets on the Lie algebras \(e(3)\) and \(so(4)\) ⋮ On one approach to the qualitative analysis of nonlinear dynamical systems ⋮ High-order conservative discretizations for some cases of the rigid body motion ⋮ On the regular precessions of an asymmetric liquid-filled rigid body ⋮ Separation of variables for a pair of integrable systems on \(\mathrm{so}^*(4)\) ⋮ Linear invariant relations of Kirchhoff's equations ⋮ Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket ⋮ Partial linear integrals of the Poincaré-Zhukovskiĭ equations (the general case) ⋮ On bi-hamiltonian structure of some integrable systems ⋮ On Invariant Manifolds of Dynamical Systems in Lie Algebras ⋮ Unnamed Item

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