Integrability of the motion of a rolling disk of finite thickness on a rough plane |
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| Affiliation: | 1. Department of Mechanical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark;2. Department of Electrical Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark;1. School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Bundoora East, VIC 3083, Australia;2. School of Mechanical Engineering, Tianjin University, Tianjin, PR China;1. Department of Mechanical Engineering, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan;2. Department of Mechanical Engineering and Science, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan;1. Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milan, Italy;2. Team CARDAMOM, INRIA Bordeaux Sud-Ouest, Talence, 33405 Cedex, France |
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| Abstract: | In this article an analytical solution of equations of motion of a rigid disk of finite thickness rolling on its edge on a perfectly rough horizontal plane under the action of gravity is given. The solution is given in terms of Gauss hypergeometric functions. The integrability results are used to construct various bifurcation diagrams of the steady motion of the disk. The bifurcations of the steady motion of a disk on a rough plane complements the author's bifurcation analysis of the steady motion of the disk on a smooth plane ( [M. Batista, Steady motion of a rigid disk of finite thickness on a horizontal plane, Int. J. Non-Linear Mech. 41 (4) (2006) 605–621]). |
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