Soluciones de equilibrio en un problema generalizado del de Lagrange-Poisson: condiciones necesarias y suficientes de estabilidad

Abstract

In this paper, we consider the problem of motion of a symmetrical gyrostat with a fixed point in a Newtonian force field, where the potential function adopts the form U = U(K3), the gyrostatic momentum and the position vector of the center of mass are on the axis of symmetry. First, we obtain the equilibrium positions of this problem; then, by means of the Energy-Casimir method, we give sufficient conditions of stability for some of these equilibria and, by spectral methods, we obtain necessary conditions of stability. The obtained results generalize the previous papers [7], [8],[9], [1] and [2].