STABILITY ON THE MANIFOLD OF EQUILIBRIUM STATES WITH SMALL VIBRATIONS OF SPACE MANIPULATORS

Stability of a planar free floating manipulator is studied on the manifold of equilibrium states. Considering the nonholonomic constraints of conservation equations for moment of momentum, Lagrange equations with multiplier are established. Hurwitz criterion is constructed to decide stability on the manifold of equilibrium states. Discrete numerical simulations show that on most points of the manifold of equilibrium states the system is unstable and that only on some special initial conditions there are few stable equilibrium points. Considering the complexity and nonlinearity, the disturbed stable equilibrium manifold and the disturbed unstable equilibrium manifold may be tangled to form a chaotic region.