The aerodynamics Influence on the Relative Motion of the Orbital System of the Two Connected Bodies. Part 1. Regular Motions

The orbital system of the two 'connected bodies' - two material points connected with the ideal flexible weightless unextensible tether - is considered as a system with the releasing constraint. Equations of the free and bounded motion as well the condition of the constraint release taking into consideration forces of the gravitational gradient, aerodynamic pressure, aerodynamic gradient and gravitational gradient and the aerodynamic pressure. Their influence on the set of the possible motion trajectories is considered. Impact less trajectories, periodic trajectories with the impacts, chaotic trajectories are found. The evolution of the phase portrait of the problem in dependence of the parameters change was studied.