Estabilidad de dos soluciones de equilibrio de un giróstato triaxial con un punto fijo en un campo de potencial U(3)

Abstract

We consider the problem of motion of a triaxial gyrostat with a fixed point in a Newtonian force field when the potential function is approximated by U(3). First, we give sufficient and necessary conditions for the existence of two equilibrium solutions. Then, by means of the Energy-Casimir method, we obtain sufficient conditions for the stability of the above equilibria. The obtained results generalize other previous results for rigid bodies or gyrostats in [9], [10], [1] , [2] and [7]. This method presents the advantage of being easy to use; in other way the problem is very difficult because of the complicated expression of the potential function.