The rolling motion of a truncated ball without slipping and spinning on a plane
- Authors: Kilin A.A.1,2, Pivovarova E.N.1
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Affiliations:
- Udmurt State University
- Institute of Mathematics and Mechanics of the Ural Branch of RAS
- Issue: Vol 22, No 3 (2017)
- Pages: 298-317
- Section: Article
- URL: https://journals.rcsi.science/1560-3547/article/view/218642
- DOI: https://doi.org/10.1134/S156035471703008X
- ID: 218642
Cite item
Abstract
This paper is concerned with the dynamics of a top in the form of a truncated ball as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system is described by differential equations with a discontinuous right-hand side. Equations describing the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation analysis of the system is made and all possible types of the top’s motion depending on the system parameters and initial conditions are defined. The system dynamics in absolute space is examined. It is shown that, except for some special cases, the trajectories of motion are bounded.
About the authors
Alexander A. Kilin
Udmurt State University; Institute of Mathematics and Mechanics of the Ural Branch of RAS
Author for correspondence.
Email: aka@rcd.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034; ul. S. Kovalevskoi 16, Ekaterinburg, 620990
Elena N. Pivovarova
Udmurt State University
Email: aka@rcd.ru
Russian Federation, ul. Universitetskaya 1, Izhevsk, 426034