Estabilidad de ciertos equilibrios de un giróstato simétrico bajo un potencial con simetría axial U(K3).

Abstract

In this paper, we consider the study of the stability of some equilibria of a symmetrical gyrostat with a fixed point in a Newtonian force field, where the potential function adopts the form U = U(K3). The Energy-Casimir method allows us to obtain sufficient conditions of stability for these equilibria. The obtained results generalize, in part, others of the papers [7], [8], [1] and [2]. In particular, these results can be applied to the case of a symmetrical gyrostat when the potential function is approximated by U(3) and to other problems, as the problem of a rigid body or gyrostat into a incomprehensible fluid.