Singular perturbation equations for flexible satellites
Abstract
Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of Ncoupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dualspin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.
 Publication:

International Journal of Non Linear Mechanics
 Pub Date:
 1980
 DOI:
 10.1016/00207462(80)900219
 Bibcode:
 1980IJNLM..15..355H
 Keywords:

 Elastic Bodies;
 Equations Of Motion;
 Flexible Spacecraft;
 Perturbation Theory;
 Structural Members;
 Structural Stability;
 Angular Velocity;
 Continuum Mechanics;
 Dynamic Models;
 Linear Equations;
 Partial Differential Equations;
 Astrodynamics