Biaxial Rotations of a Satellite in its Orbit Plane.
Abstract:
Mode of a satellite attitude motion, named biaxial rotation in an orbit plane, is investigated. A satellite is supposed to be close to dynamic symmetric one. It rotates around its longitudinal axis, which in turn rotates around normal to the orbit plane; the angular rate of the longitudinal axis is greater by several fold the orbital mean motion, the deviation of that axis from the orbit plane is small. The investigation is based on the assumptions that the satellite is a rigid body affected by the gravitational torque and its orbit is fixed and circular. Undisturbed biaxial rotations are described by a formal four-dimensional integral manifold stratified onto two-dimensional invariant tori. The periodic solutions exist in arbitrary vicinities of the tori. Analysis of those periodic solutions is a way of studying of undisturbed biaxial rotations. Another way consists in construction of Poincare mappings. Both ways are implemented. One-parametric families of symmetric periodic solutions, close to the tori, are calculated and their stability in linear approximation is investigated. Stroboscopic pictures are constructed for visualizing iterations of Poincare mapping.
