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March  2010, 3(1): 85-103. doi: 10.3934/dcdss.2010.3.85

Nonlinear dynamics and stability of the skateboard

Andrey V. Kremnev 1, and  Alexander S. Kuleshov 1,

1. 

Department of Mechanics and Mathematics, Moscow State University, Main building of MSU, Leninskie Gory, Moscow, 119991, Russian Federation, Russian Federation

Received  June 2008 Revised  November 2008 Published  December 2009

In this paper the further investigation and development for the simplified mathematical model of a skateboard with a rider are obtained. This model was first proposed by Mont Hubbard [12, 13]. It is supposed that there is no rider’s control of the skateboard motion. To derive equations of motion of the skateboard the Gibbs-Appell method is used. The problem of integrability of the obtained equations is studied and their stability analysis is fulfilled. The effect of varying vehicle parameters on dynamics and stability of its motion is examined.
Keywords: Skateboard; Nonholonomic Constraints; Gibbs-Appell equations; Stability of Motion..
Mathematics Subject Classification: Primary: 70F25, 70E18; Secondary: 70E40, 70E5.
Citation: Andrey V. Kremnev, Alexander S. Kuleshov. Nonlinear dynamics and stability of the skateboard. Discrete and Continuous Dynamical Systems - S, 2010, 3 (1) : 85-103. doi: 10.3934/dcdss.2010.3.85
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