On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Inclusion

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Abstract

A problem of motion of a point particle on a surface of a homogeneous gravitating ball with a spherical inclusion of a differing density is considered. It is assumed that the body rotates uniformly around its symmetry axis. It is supposed that "besides the gravitation force, the particle is subjected to dry friction.

The gravitational properties outside the ball are described. The dependence of existence, bifurcations, and stability of relative equilibria of the point particle on the body surface on the parameters of the problem is studied. The results are represented both analytically and as numerically obtained bifurcation diagrams.

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About the authors

A. A. Burov

FRC CSC RAS

Author for correspondence.
Email: jtm@narod.ru
Russian Federation, Moscow

V. I. Nikonov

FRC CSC RAS

Email: nikon_v@list.ru
Russian Federation, Moscow

E. S. Shalimova

Lomonosov Moscow State University

Email: ekateryna-shalimova@yandex.ru
Russian Federation, Moscow

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