This article is cited in 4 scientific papers (total in 4 papers)
Asymptotic stability and associated problems of dynamics of falling rigid body
A. V. Borisovabc, V. V. Kozlovd, I. S. Mamaevabc
a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Udmurt State University
c Institute of Computer Science
d Steklov Mathematical Institute, Russian Academy of Sciences
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.
nonholonomic mechanics, rigid body, ideal fluid, resisting medium.
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MSC: 74F10, 93D20
A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Asymptotic stability and associated problems of dynamics of falling rigid body”, Nelin. Dinam., 3:3 (2007), 255–296
Citation in format AMSBIB
\by A.~V.~Borisov, V.~V.~Kozlov, I.~S.~Mamaev
\paper Asymptotic stability and associated problems of dynamics of falling rigid body
\jour Nelin. Dinam.
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G. E. Grishanina, N. G. Inozemtseva, B. I. Sadovnikov, “On Global Asymptotic Stability and Stability of Saddle Solutions at Infinity”, Math. Notes, 93:4 (2013), 624–628
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