On the nonlinear dynamics of a flexible structure in orbit
by
M.R.M. Crespo da Silva
Dept. of Mechanical Engrg., Aeronautical Engrg., and Mechanics; Rensselaer Polytechnic Institute; Troy, N.Y. 12180-3590

The differential equations of motion of dynamical systems are generally nonlinear. To investigate the motion of the system, it is very common practice to linearize the equations about a particular solution, such as an equilibrium solution. What is not very common among engineers is to perform investigations to determine what effect the nonlinearities have on the system dynamics. However, nonlinearities in the differential equations of motion may cause the system response to be completely different from the response predicted by linearization, even for very small initial pertubations about the corresponding equilibrium solution of the system. A mathematically rigorous analysis of the response of a long flexible structure in orbit around a planet, and the formulation of the nonlinear differential equations that govern the motion, are presented in this paper. The equations account for inertia nonlinearities, and for nonlinear terms in the expression for the curvature along the structural member. It is shown that, under certain conditions, undesirable nonlinear interactions between bending and pitching motions may be exhibited by the structure, and that such a response may grow to undesirable amplitudes after several orbits. The nonlinear response that results because of such interactions is analyzed by a perturbation technique.

Date received: January 14, 2000