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arXiv · 2405.07511

Bifurcation analysis of the problem of a "rubber" ellipsoid of revolution rolling on a plane

Alexander Kilin·Elena Pivovarova
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Abstract

This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of motion to a fixed level set of first integrals is performed. Permanent rotations corresponding to the rolling of an ellipsoid in a circle or in a straight line are found. A linear stability analysis of permanent rotations is carried out. A complete classification of possible trajectories of the reduced system is performed using a bifurcation analysis. A classification of the trajectories of the center of mass of the ellipsoid depending on parameter values and initial conditions is performed.

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Alexander Kilin, Elena Pivovarova. 2024-05-13. Bifurcation analysis of the problem of a "rubber" ellipsoid of revolution rolling on a plane. https://doi.org/10.1007/s11071-024-09863-7

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