On periodic motions of a rigid body in a central Newtonian field: PMM vol. 38, n≗2, 1974, pp. 224–227

Abstract

In the problem of the motion of a rigid body with one fixed point in a central Newtonian force field (in particular, in the de Brun field [1]).The existence of a family of periodic solutions is proved by the Poincaré method of small parameters. It is assumed that the body differs negligibly from a dynamically symmetric one and that its center of gravity is sufficiently close to the fixed point. The proof is carried out by using the techniques of Hamiltonian systems.