Dynamics of a Gravity Gradient Anchored Tethered Space Antenna

An analysis of the attitude dynamics of a tether-stabilized orbiting space antenna is presented. For many missions it is desirable to fly an antenna in space with its collecting surface nadir directed. Oriented with its large spatial dimensions perpendicular to the gravitational radius vector, an antenna body alone could well be unstable. Adding tethered masses to the antenna could stabilize the attitude by altering the system's inertial properties. The motion equations are derived for a system comprised of a rigid body and two tethered point masses in orbit about an inertially spherical gravitational primary. An arbitrary number of tethers connect the point masses to the rigid body attaching at distinct locations. A single tether is allowed to connect the respective masses. The tethers are assumed to be massless tensile members of fixed unstrained length possessing viscoelastic constitutive character. The nonlinear motion equations for the system are derived from Newton-Euler momentum principles. A steady state solution to the motion equations is proposed for the system centroid in a circular orbit. Considering small motions about the steady state configuration, the linearized motion equations are derived. The linearized equations are brought to a standard canonical form suitable for application of the stability theorems for linear stationary second order systems.