Integration of Constraint Equations in Problems of a Disc and a Ball Rolling on a Horizontal Plane

2011/07/20 by Eugeny A. Mityushov, Mityushov, Eugeny A.
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #math.DS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1107.3963

9 pages, 4 figures

arxiv created 2011/07/20 · arxiv updated 2011/07/21

Abstract

The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural equation, i.e. when the dependence of the curvature of the trajectory is explicitly expressed in terms of the distance passed by the point.

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