Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 049, 20 pages      math.CA/0605204      https://doi.org/10.3842/SIGMA.2006.049

On One Approach to Investigation of Mechanical Systems

Valentin D. Irtegov and Tatyana N. Titorenko
Institute for Systems Dynamics and Control Theory, SB RAS, Irkutsk, Russia

Received November 18, 2005, in final form April 11, 2006; Published online May 08, 2006

Abstract
The paper presents some results of qualitative analysis of Kirchhoff's differential equations describing motion of a rigid body in ideal fluid in Sokolov's case. The research methods are based on Lyapunov's classical results. Methods of computer algebra implemented in the computer algebra system (CAS) "Mathematica" were also used. Combination of these methods allowed us to obtain rather detailed information on qualitative properties for some classes of solutions of the equations.

Key words: rigid body mechanics; completely integrable systems; qualitative analysis; invariant manifolds; stability; bifurcations; computer algebra.

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