Deformable Asymmetric Tops under Similarity Transformations

In this paper the configurations of relative equilibrium are determined for a deformable heavy top with a fixed point constrained to deform only by similarity transformations. We analyze the nonlinear orbital stability using the reduced energy–momentum method for configurations such that the center of the mass vector is parallel to the axis of gravity and coincides with an eigenvector of the Euler tensor. In addition, we study these conditions of stability for a specific deformable top given by a hyperelastic material of the Saint Venant–Kirchhoff type, and describe how these conditions are particularized in the special case of almost rigid tops.