The separatrix of an unstable position of equilibrium of a Hess-Appelrot gyroscope
A heavy rigid body rotating about a fixed point, whose inertial tensor and the centre of mass satisfy the Hess-Appelrot conditions, is considered. The gyroscope has an unstable position of equilibrium at which the radius-vector from the point of support to the centre of mass is directed vertically upwards at the zeroth value of area integral constant. The motion close to the paired separatrices is considered, and a set of long-period solutions are obtained. The splitting of the separatrices of perturbed unstable permanent rotation is studied using first-order perturbation theory. The same problem for a perturbed Lagrange gyroscope is discussed as a special case of Hess-Appelrote gyroscope.
scientific article; zbMATH DE number 500932