%0 Journal Article %A Vera López, Juan Antonio %A Vigueras Campuzano, Antonio %T Soluciones de equilibrio en un problema generalizado del de Lagrange-Poisson: condiciones necesarias y suficientes de estabilidad %D 2003 %@ 1132-6360 %U http://hdl.handle.net/10317/1419 %X 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]. %K Matemática Aplicada %K Giróstato simétrico %K Análisis espectral %K Estabilidad espectral %K Ecuaciones de Lie-Poisson %K Energía-Casimir %K Symmetric gyrostat %K Spectral analysis %K Spectral stability %K Lie-Poisson equation %K Energy-Casimir %~ GOEDOC, SUB GOETTINGEN