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On Some Results of Investigation of Kirchhoff Equations in Case of a Rigid Body Motion in Fluid

  • Valentin Irtegov
  • Tatyana Titorenko
Conference paper
  • 641 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)

Abstract

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].

Keywords

Lyapunov Function Invariant Manifold Rigid Body Motion Computer Algebra System Nonlinear Algebraic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Valentin Irtegov
    • 1
  • Tatyana Titorenko
    • 1
  1. 1.Institute of Systems Dynamics and Control Theory, SB RASIrkutskRussia

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