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

A. A. Burov; Буров А. А.; V. I. Nikonov; Никонов В. И.; E. S. Shalimova; Шалимова Е. С.

doi:10.31857/S0032823524020016

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

Authors: Burov A.A.¹, Nikonov V.I.¹, Shalimova E.S.²
Affiliations:
1. FRC CSC RAS
2. Lomonosov Moscow State University
Issue: Vol 88, No 2 (2024)
Pages: 172-189
Section: Articles
URL: https://kazanmedjournal.ru/0032-8235/article/view/675061
DOI: https://doi.org/10.31857/S0032823524020016
EDN: https://elibrary.ru/XVNMMG
ID: 675061

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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.

Keywords

dynamics on surfaces of celestial bodies, celestical bodies with cavities, relative equilibria, dry friction, motion of a point particle in a noncentral gravity field, generalization of a gravitating dumbbell, mascons

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