Classification of integrable quadratic Hamiltonians on e(3)

Please always quote using this URN: urn:nbn:de:0297-zib-11807
  • Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed.

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Metadaten
Author:Thomas Wolf, Olya V. Efimovskaya
Document Type:ZIB-Report
Tag:Kowalevski type Hamiltonians; Linear Poisson brackets on e(3); first integrals; rigid body dynamics
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] / 37J35 Completely integrable systems, topological structure of phase space, integration methods
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] / 37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Nxx Applications / 37N15 Dynamical systems in solid mechanics [See mainly 74Hxx]
PACS-Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.40.-k Geometry, differential geometry, and topology (see also section 04 Relativity and gravitation) / 02.40.Yy Geometric mechanics (see also 45.20.Jj in formalisms in classical mechanics)
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.70.-c Computational techniques; simulations (for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics) / 02.70.Wz Symbolic computation (computer algebra)
Contributing Corporation:Brock University, St.Catharines, Canada and ZIB Fellow; Moscow State University
Date of first Publication:2010/07/07
Series (Serial Number):ZIB-Report (10-18)
ISSN:1438-0064
Published in:Appeared in: Regular and Chaotic Dynamics, vol 8, no 2 (2003), p 155-162