Integrable quadratic Hamiltonians on so(4) and so(3,1)

Please always quote using this URN: urn:nbn:de:0297-zib-8085

We investigate a special class of quadratic Hamiltonians on $so(4)$ and $so(3,1)$ and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.

Metadaten
Author:	Vladimir V. Sokolov, Thomas Wolf
Document Type:	ZIB-Report
Tag:	classification; integrable quadratic Hamiltonians; polynomial integrals
MSC-Classification:	34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Mxx Differential equations in the complex domain [See also 30Dxx, 32G34] / 34M55 Painlevé and other special equations; classification, hierarchies;
	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] / 37Nxx Applications / 37N15 Dynamical systems in solid mechanics [See mainly 74Hxx]
Date of first Publication:	2004/08/11
Series (Serial Number):	ZIB-Report (04-33)
ArXiv Id:	http://arxiv.org/abs/nlin.SI/0405066
ZIB-Reportnumber:	04-33
Published in:	Appeared in: J. Phys. A: Math. Gen., 39 (2006), pp. 1915-1926

Open Access