Generalization of the Goryachev-Chaplygin Case

Details Generalization of the Goryachev-Chaplygin Case Generalization of the Goryachev-Chaplygin Case

2003-02-28

arxiv.org/abs/nlin/0302062v1

Regular and Chaotic Dynamics, V.7, #1, 2002, p.21-30

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages

Scientific paper

In this paper we present a generalization of the Goryachev-Chaplygin integrable case on a bundle of Poisson brackets, and on Sokolov terms in his new integrable case of Kirchhoff equations. We also present a new analogous integrable case for the quaternion form of rigid body dynamics' equations. This form of equations is recently developed and we can use it for the description of rigid body motions in specific force fields, and for the study of different problems of quantum mechanics. In addition we present new invariant relations in the considered problems.

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