Comparison of melnikov's method and numericla simulation for predicting nonlinear dynamics in the pitch motion of actively controlled satellites in a gravity gradient field

摘要

In this work we study the pitch dynamics of an actively-controlled, gravity gradient spacecraft in an elliptical orbit about a central body. We outline previous analytical results derived using a higher-dimensional version of Melnikov's method which predicts those sets of system parameters for which the dynamics of the system may be chaotic. We compare those results with extensive numerical simultaions to ascertain he validity of our Melnikov analysis. As a result of our numerical analysis, we not only discover the types of behavior that can occur in this system, but demonstrate the efficacy of using Melnikov's method to predict those values of the systems parameters which can potnetially lead to undesirable dynamics. This work is the first of which we are aware to compare numerical simulations with the higher-dimensional version of Melnikov's method.