Application of Modified Chebyshev Picard Iteration to the Relative Orbital Dynamics Problem

Abstract

In this paper we apply the Modified Chebyshev Picard Iteration Method, which uses Chebyshev Polynomials as basis functions to the Orbital Relative Dynamics Problem. We use the mathematical properties of the Chebyshev polynomials to speed up the integration process by parallel problem solving. In this paper we will only apply this method to the Clohessy-Wiltshire model of satellite relative motion, as their is a analytical solution available so we can easily quantify our results in comparison to the analytical method and other numerical methods like ODE45 and ODE113.