Two-cable System “Dumbbell-load” in the Central Gravitational Field Maria Munitsyna (Moscow)

Generalized coordinates : Nxy- fixed coordinates, N- gravitating center, O- center of mass system “dumbbell-load” C- center of mass dumbbell

«tangent » stationary motions «triangled » stationary motions Free motion

«tangent » stationary motions «triangled » stationary motions Half-connected motion

« radial » stationary motions Half-connected motion

phase-plane portrait Connected motion

Conclusion Three types of system’s motion are defined depending on cables tension (free motion, half-connected motion and connected motion) On the basis of the Raus’ theory the system order is lowered and stationary motions are defined for all cases of motions off the systems For obtained connected and half-connected motion the condition of constraints tension is checked Depending on system’s parameters stability and bifurcation of obtained solutions are investigated. The results are presented in the form of bifurcation diagrams. In the case of connected motion geometric interpretation of motion is given. Phase-plane portrait of system is constructed, the regions of impossibility of connected motion is obtained. Obtained results may be used for changes and stabilization equilibrium satellite orientation on the orbit.