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I. Mamaev (2003)
NEW CASES WHEN THE INVARIANT MEASURE AND FIRST INTEGRALS EXIST IN THE PROBLEM OF A BODY ROLLING ON A SURFACE
Yu.D. Glukhikh, V.N. Tkhai, D.P. Chevallier (2000)
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(1992)
New Cases of the Existence of an Integral Invariant in a Problem on the Rolling of a Rigid Body, Without Slippage, on a Fixed Surface
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.
Regular and Chaotic Dynamics – Springer Journals
Published: Aug 31, 2008
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