Stationary solutions of a small gyrostat in the Newtonian field of two bodies with equal masses

Abstract

To cite this version:Tilemahos J. Kalvouridis. Stationary solutions of a small gyrostat in the Newtonian field of two bodies with equal masses. Nonlinear Dynamics, Springer Verlag Abstract The paper deals with the dynamics of a small gyrostat satellite acted upon by the Newtonian forces of two big bodies of equal masses which rotate around their center of mass. The gyrostat's equations of motion are derived and classes of its stationary solutions, as well as their stability are studied.

Stability of the permanent rotations of an asymmetric gyrostat in a uniform Newtonian field

“…A further step in the complexity of the problem, and in the approximation to a real one, is to consider the motion of a gyrostat under the attraction of a Newtonian field. For this problem, some authors have found approximated analytical solutions for particular cases [7,32] and other authors have studied the equilibria and their stability when the gyrostat is in circular orbit [33,34] or in the gravity field of a number of di↵erent rigid bodies [21,35]. In this paper we focus on the stability of permanent rotations of a heavy gyrostat with a fixed point, that is to say when the gyrostat is under a uniform gravity field.…”

Gyrostat Model Regular And Chaotic Behavior

“…The gyroscope has attributes of great utility to navigational and aeronautical engineering, biology, optics, etc. [3][4][5][6][7][8]. Different types of gyroscopes (with linear or nonlinear damping, fluid, etc.)…”