Dynamics of rolling disk
A.V. Borisov, I.S. Mamaev, A.A. Kilin
TL;DR
This paper provides a qualitative analysis of the rolling motion of a homogeneous disk on a plane, exploring contact point trajectories, integrability, and bifurcation diagrams to understand its dynamics.
Contribution
It offers new insights into the contact point trajectories and bifurcation structures of a rolling disk, extending classical results with detailed qualitative analysis.
Findings
Contact point trajectories can be finite or infinite.
Bifurcation diagrams reveal stability regions.
Conditions for integrability are discussed.
Abstract
In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. The problem was studied by S.A. Chaplygin, P. Appel and D. Korteweg who showed its integrability. The behavior of the point of contact on a plane is investigated and conditions under which its trajectory is finit are obtained. The bifurcation diagrams are constructed.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Control and Dynamics of Mobile Robots