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Asymptotic stability and associated problems of dynamics of falling rigid body

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Abstract

We consider two problems from the rigid body dynamics and use new methods of stability and asymptotic behavior analysis for their solution. The first problem deals with motion of a rigid body in an unbounded volume of ideal fluid with zero vorticity. The second problem, having similar asymptotic behavior, is concerned with motion of a sleigh on an inclined plane. The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. A comprehensive survey of references is given and new problems connected with falling motion of heavy bodies in fluid are proposed.

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  1. Institute of Computer Science, Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russia

    A. V. Borisov & I. S. Mamaev

  2. V.A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. V. Kozlov

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  1. A. V. Borisov
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  3. I. S. Mamaev
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Borisov, A.V., Kozlov, V.V. & Mamaev, I.S. Asymptotic stability and associated problems of dynamics of falling rigid body. Regul. Chaot. Dyn. 12, 531–565 (2007). https://doi.org/10.1134/S1560354707050061

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