Analysis of Space Station Motion Subject to the Parametric Excitation of Periodic Elevator Motion

摘要

This study will derive the equations of attitude motion for a gravity gradient stabilized space station whose moments of inertia are varying with time. The equations are then linearized, after which an analytical solution of the pitch equation is developed. An examination of the stability of motion for the resulting Hill equation is presented and then compared to the solution obtained from numerical integration of the nonlinear equations. The results show that for elevator frequencies on the order of the orbit rate, motion can grow unboundedly with time. Consequently, the shape of the classical Lagrange stability region is altered. Keywords: motion sickness; aerospace medicine; mathematical models; theses.