This article is cited in 10 papers

On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)

Alexander A. Burov^ab, Ekaterina S. Shalimova<sup>c

a</sup> Dorodnicyn Computing center of the RAS, ul. Vavilova 40, Moscow
^b Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000 Russia
^c Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia

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.

MSC: 70F40, 70K42, 70K50

Received: 10.01.2015

Language: English

DOI: 10.1134/S1560354715030028

Bibliographic databases:

• 
• 
• 
• 
• 
•