Regular and Chaotic Dynamics

, Volume 13, Issue 4, pp 239–249 | Cite as

Stability of steady rotations in the nonholonomic Routh problem

Nonholonomic Mechanics

Abstract

We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball at the upmost, downmost and saddle point.

Key words

nonholonomic constraint stationary rotations stability 

MSC2000 numbers

34D20 70E40 37J35 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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