Geodesic
Asymptotic stability and associated problems of dynamics of falling rigid body
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 3, pp. 255-296

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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.
Keywords: nonholonomic mechanics, rigid body, ideal fluid, resisting medium. 
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     author = {A. V. Borisov and V. V. Kozlov and I. S. Mamaev},
     title = {Asymptotic stability and associated problems of dynamics of falling rigid body},
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     pages = {255--296},
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     url = {http://geodesic.mathdoc.fr/item/ND_2007_3_3_a1/}
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A. V. Borisov; V. V. Kozlov; I. S. Mamaev. Asymptotic stability and associated problems of dynamics of falling rigid body. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 3, pp. 255-296. http://geodesic.mathdoc.fr/item/ND_2007_3_3_a1/