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2013
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# Alexandr Kuleshov

Moscow, 119899, Vorobievy gory
Departament of Mechanics and Mathematics Moscow State University

## Publications:

 Kuleshov A. S. Further Development of the Mathematical Model of a Snakeboard 2007, vol. 12, no. 3, pp.  321-334 Abstract This paper gives the further development for the mathematical model of a derivative of a skateboard known as the snakeboard. As against to the model, proposed by Lewis et al. [13] and investigated by various methods in [1]-[13], our model takes into account an opportunity that platforms of a snakeboard can rotate independently from each other. This assumption has been made earlier only by Golubev [13]. Equations of motion of the model are derived in the Gibbs–Appell form. Analytical and numerical investigations of these equations are fulfilled assuming harmonic excitations of the rotor and platforms angles. The basic snakeboard gaits are analyzed and shown to result from certain resonances in the rotor and platforms angle frequencies. All the obtained theoretical results are confirmed by numerical experiments. Keywords: Snakeboard, Gibbs–Appell equations, dynamics, analysis of motion Citation: Kuleshov A. S.,  Further Development of the Mathematical Model of a Snakeboard, Regular and Chaotic Dynamics, 2007, vol. 12, no. 3, pp. 321-334 DOI:10.1134/S1560354707030045
 Karapetyan A. V., Kuleshov A. S. Steady Motions of Nonholonomic Systems 2002, vol. 7, no. 1, pp.  81-117 Abstract In this review we discuss methods of investigation of steady motions of nonholonomic mechanical systems. General conclusions are illustrated by examples from the rigid bodies dynamics on a absolutely rough horisontal plane. Citation: Karapetyan A. V., Kuleshov A. S.,  Steady Motions of Nonholonomic Systems, Regular and Chaotic Dynamics, 2002, vol. 7, no. 1, pp. 81-117 DOI:10.1070/RD2002v007n01ABEH000198
 Kuleshov A. S. On the Generalized Chaplygin Integral 2001, vol. 6, no. 2, pp.  227-232 Abstract The problem of the motion of a rotational symmetric rigid body along a perfectly rough surface is considered. The conditions of existence of a Chaplygin-type integral are obtained. It is shown, that these conditions are valid in the case of the motion of a nonhomogeneous dynamically symmetric sphere along a perfectly rough plane or along the internal surface of a sphere. Citation: Kuleshov A. S.,  On the Generalized Chaplygin Integral, Regular and Chaotic Dynamics, 2001, vol. 6, no. 2, pp. 227-232 DOI:10.1070/RD2001v006n02ABEH000173