Bifurcation of equilibria for general case of gyrostat satellite on a circular orbit

Abstract

This paper is on the study of the Equilibria of a Gyrostat Satellite on a Circular Orbit when its angular momentum it’s not aligned with any principal axis or when the angular momentum is not aligned with orbital coordinate frame stated in this paper as the general case. This study is conducted to achieve through the use of Euler angles which are developed into achieving through the use of the Resultant method a unique polynomial equation in function of four adimensional parameters, which its roots are directly proportional to the number of equilibria positions. Through the development of the algorithm and the analysis of the equilibria positions it was achieved a simple analytic expression for the same number of equilibria positions. It was also verified the existence of small regions of equilibria out of their main area near when the angular momentum is in a principal plane as expected to be found when the angular momentum is in a principal plane.