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].
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Irtegov, V., Titorenko, T. (2005). On Some Results of Investigation of Kirchhoff Equations in Case of a Rigid Body Motion in Fluid. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_22
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DOI: https://doi.org/10.1007/11555964_22
Publisher Name: Springer, Berlin, Heidelberg
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