Ekaterina Shalimova

Address: Leninskie Gory 1, Moscow, 119991 Russia

University: Lomonosov Moscow State University

Publications:

Burov A. A., Shalimova E. S.

On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)
2015, vol. 20, no. 3, pp. 225-233

Abstract

The problem of motion of a heavy particle on a sphere uniformly rotating about a fixed axis is considered in the case of dry friction. It is assumed that the angle of inclination of the rotation axis is constant. The existence of equilibria in an absolute coordinate system and their linear stability are discussed. The equilibria in a relative coordinate system rotating with the sphere are also studied. These equilibria are generally nonisolated. The dependence of the equilibrium sets of this kind on the system parameters is also considered.

Keywords: dry friction, motion of a particle on a sphere, absolute and relative equilibria, bifurcations of equilibria

Citation: Burov A. A., Shalimova E. S., On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case), Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 225-233

DOI:10.1134/S1560354715030028

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