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Two-cable System “Dumbbell-load” in the Central Gravitational Field

Two-cable System “Dumbbell-load” in the Central Gravitational Field. Maria Munitsyna (Moscow). Nxy- fixed coordinates , N- gravitating center , O- center of mass system “dumbbell-load” C- center of mass dumbbell. G eneralized coordinates :.

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Two-cable System “Dumbbell-load” in the Central Gravitational Field

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

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

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

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

  5. Half-connected motion «radial» stationary motions

  6. Connected motion phase-plane portrait

  7. 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.

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