Integrable quadratic Hamiltonians with a linear Lie-Poisson bracket

Please always quote using this URN: urn:nbn:de:0297-zib-8414

Quadratic Hamiltonians with a linear Lie-Poisson bracket have a number of applications in mechanics. For example, the Lie-Poisson bracket $e(3)$ includes the Euler-Poinsot model describing motion of a rigid body around a fixed point under gravity and the Kirchhoff model describes the motion of a rigid body in ideal fluid. Advances in computer algebra algorithms, in implementations and hardware, together allow the computation of Hamiltonians with higher degree first integrals providing new results in the search for integrable models. A computer algebra module enabling related computations in a 3-dimensional vector formalism is described.

Metadaten
Author:	Thomas Wolf
Document Type:	ZIB-Report
Tag:	Computer algebra; Hamilton systems; Integrability
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:	2005/01/14
Series (Serial Number):	ZIB-Report (05-07)
ZIB-Reportnumber:	05-07
Published in:	Appeared in: Gen. Relativ. Gravit. 38, no 6(2006), pp. 1115-1127.
DOI:	https://doi.org/10.1007/s10714-006-0293-2

Open Access