Application of Singular Perturbation Theory to Space Flight Dynamics Problems

Singular perturbation theory is applied for analytically determining the first-order effects of small acceleration terms on spacecraft orbital dynamics, which are representative of the action of a drag force or of an electric low-thrust propulsion system. The effects of density variation with altitude and thrust magnitude as a function of distance from the primary body are included in the analysis. Numerical integration demonstrates the validity of the analytical results in predicting the secular variation of orbit parameters in planar motion.