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Asymptotic stability and associated problems of dynamics of falling rigid body. (English) Zbl 1229.37107
Summary: 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.

MSC:
37N05 Dynamical systems in classical and celestial mechanics
37J60 Nonholonomic dynamical systems
70E15 Free motion of a rigid body
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