Abstract
A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented. For small elastic displacements and attitude angles the linearized equations for the roll and yaw (out-of-plane) motions completely separate from the pitch (in-plane) and elastic motions. However, the pitch and only the axisymmetric elastic modes are seen to be coupled in the linear range. With the shell's symmetry axis following the local vertical, the structure undergoes a static deformation under the influence of gravity and inertia. Further, the pitch and roll motions are unstable due to the unfavorable moment of inertia distribution. A rigid dumbbell connected to the shell at its apex by a spring-loaded double-gimball joint is proposed to stabilize the structure gravitationally. A sensitivity study of the system response characteristics to the key system parameters is carried out.
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