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首页> 外文会议>International Workshop on Computer Algebra in Scientific Computing(CASC 2005); 20050912-16; Kalamata(GR) >On Some Results of Investigation of Kirchhoff Equations in Case of a Rigid Body Motion in Fluid
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On Some Results of Investigation of Kirchhoff Equations in Case of a Rigid Body Motion in Fluid

机译：关于流体中刚体运动情况下Kirchhoff方程研究的一些结果

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摘要

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. The computer algebra systems (CAS) "Mathematica", "Maple", and a software 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.
机译：给出了描述理想状态下不可压缩流体中刚体运动的Kirchhoff方程分析的一些结果。关于这些方程式，提出了一个问题，以获得稳态运动，稳态运动的不变流形（IMSM），并研究运动的稳定性和稳定性方面的特性。我们的调查方法基于Lyapunov获得的经典结果。工具使用计算机代数系统（CAS）“ Mathematica”，“ Maple”和软件。对于获得的某些稳态运动，导出了李雅普诺夫的充分稳定性条件。对于不稳定运动的某些情况，解决了关于一阶近似方程的最佳稳定问题。本文代表了我们研究的延续，其结果已在2004年CASC'圣彼得堡会议上报告。

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