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

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


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].


Lyapunov Function Invariant Manifold Rigid Body Motion Computer Algebra System Nonlinear Algebraic Equation 
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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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