Nonlinear Models of Relative Dynamics

Abstract

This chapter presents commonly used nonlinear models for relative perturbed and unperturbed motion. The chapter presents a variety of models for simulating relative motion in perturbed or unperturbed elliptic orbits. In the absence of perturbations, bounded relative motion between any two spacecrafts in elliptic Keplerian orbits can be straightforwardly found from the energy matching condition. This chapter suggests a rather simple method for generating bounded relative motion between any two spacecrafts for unperturbed Keplerian motion. The underlying methodology relies on the concept of orbital-period commensurability. The chapter presents a single-impulse formation-keeping method by using the inherent freedom of the energy matching condition. The chapter provides an insight into the resulting formation-keeping maneuver by utilizing the classical orbital elements. The chapter elaborates the energy matching condition, and equations of relative motion under the influence of J2. A simple framework is designed for both initialization and initialization-error correction for spacecraft formation flying. This framework yields bounded relative motion between any two spacecraft flying on arbitrary elliptic orbits. The chapter also introduces a set of useful transformations for converting the relative motion states between the L and I frames.