Alexander Rodnikov

In this paper we study the following problem. Let a particle move in a central Newtonian gravitational field near a massive gravitationally oriented body. The body describes a circular orbit and is equipped with a "leier constraint", i.e. a cable with both ends fixed on the body (from the Dutch maritime term "leier"— a rope with both ends fixed). We study the possibility of capturing the particle (i.e. to force the particle to move periodically) by a gripper coasting on the "leier constraint". Any discontinuities in the velocity and acceleration are not allowed. We show that using a sufficiently long cable the capture is possible for almost all values of the system parameters. We also construct a modified algorithm that allows many-fold reduction in the required cable length.

The perturbed canonical equations of the problem of celestial body rotation about its center of mass are considered. Solutions are constructed via Hori's method [1]. All the operations of the method mentioned are prepared as simple action over Poisson's series depending on several variables which are based on Andoyer's angles and integrals of the unperturbed problem. Such variables are defined for a nonsymmetric rigid body and for a symmetric magnetised satellite of the Earth. In the first case variables mentioned are constructed by means of Poinsot's geometrical interpretation of the motion. In the second case these are built through intermediate canonical transformations that transfer the top of some hyperbolid to a point that corresponds to a regular precession of the satellite.