ISSN 1560-3547, Regular and Chaotic Dynamics, 2011, Vol. ... MSC2010 numbers: 34D20, 70E40, 37J35 DOI: 10.1134/S1560354711060062 Keywords: billiard, impact, point map, nonintegrability, periodic solution, nonholonomic constraint, integral of motion 1. ... 2 Vol. ... Then if one of the semi-axes of the cylinder's base tends to zero (b2 0) we get the problem on nonholonomic bil liard inside a flat strip with the fol lowing law of reflection 0 0 -1 = 0 cos - sin 0 - sin - cos V where V = (vn , v , ua ). ...

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