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On some results of investigation of Kirchhoff equations in case of a rigid body motion in fluid

Авторы: Irtegov V., Titorenko T.

Журнал: Lecture Notes in Computer Science

Том: 3718

Номер:

Год: 2005

Отчётный год: 2005

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Аннотация: Some results of analysis of Kirchhoff equations, which describe the motion of a rigid body in the ideal incompressible fluid, are presented. With respect to these equations, a problem is stated to obtain steady-state motions, invariant manifolds of steady-state motions (IMSMs), and to investigate their properties in the aspect of stability and stabilization of motion. Our methods of investigation are based on classical results obtained by Lyapunov [1]. The computer algebra systems (CAS) "Mathematica", "Maple", and a software [2] are used as the tools. Lyapunov's sufficient stability conditions are derived for some steady-state motions obtained. A problem of optimal stabilization with respect to the first approximation equations is solved for some cases of unstable motion. This paper represents a continuation of our research, the results of which have been reported during CASC'2004 in St. Petersburg [3].

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