Intersection of asymptotic surfaces of the perturbed euler-poinsot problem

Abstract

The mutual disposition of the asymptotic surfaces (separatrices) of perturbed permanent rotations is considered in the problem of the motion of an asymmetric heavy rigid body with a fixed point in a weak gravitational field. It is shown that, for small values of the Poincaré parameter, there are always no paired separatrices, except in the Hess-Appelroth case. As the Poincaré parameter tends to zero, it is shown that an infinite number of bifurcations of the birth and disappearance of heteroclinic solutions, passing close to the three undisturbed separatrices, can be observed.