Stability of steady rotations in the nonholonomic Routh problem
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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 wordsnonholonomic constraint stationary rotations stability
MSC2000 numbers34D20 70E40 37J35
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