Perturbed pendulum motions of a rigid body about a fixed point

This paper is devoted to a detailed investigation of the perturbed pendulum motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are introduced. Characteristic properties of perturbed pendulum motions of the body in inertial space are studied. A qualitative description of asymptotics of pendulum motions in a neighbourhood of split separatrices is given.