Regular and Chaotic Dynamics

, Volume 12, Issue 5, pp 531–565 | Cite as

Asymptotic stability and associated problems of dynamics of falling rigid body

150th Anniversary of A.M. Lyapunov

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.

Key words

rigid body ideal fluid non-holonomic mechanics 

MSC2000 numbers

37 J60 

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Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia
  2. 2.V.A. Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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