Analysis of the gyroscope motion in the canonical variables Andoyer-Deprit

The researches of movement of gyroscopes are still one of the main problems of the dynamics of a rigid body and its systems. It also has a major importance for applied problems of a space-flight mechanics. Now there is a research investigation of rotation of gyroscope in Hess' conditions. Motion equations of a solid body are determined on the base of Hamiltonian formalism. There are some analytical researches and computer experiments were made on the base of numeral study of phase portrait of equations, which describe gyroscope's motion. The movements of gyroscope, which is submitted to Hess' conditions in the null constant of integral of an area and a light weight of the body, are investigated more in details. The motion equations and integrals are expressed in the variables Andoyer-Deprit. The heteroclinic trajectories of the dynamical system are examined with the help of the new canonical variables.