On detachment conditions in the problem on the motion of a rigid body on a rough plane
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In the absence of friction, the detachment conditions on stationary motions do not hold. However, if the angle θ between the symmetry axis and the vertical decreases to zero, motions close to stationary motions are necessarily accompanied by detachments.
The same conclusion holds for a thin disk that rolls on the support without sliding.
For a disk of nonzero thickness in the absence of sliding, the detachment conditions hold on stationary motions in some domain in the space of parameters; in this case, the angle θ is not less than 49 degrees. For small values of θ, the contact between the body and the support does not break in a neighborhood of stationary motions.
Key wordsunilateral constraint friction Painlevé paradoxes
MSC2000 numbers70E18 70E50 70G70
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