Using Newton’s Method to Search for Quasi-Periodic Relative Satellite Motion Based on Nonlinear Hamiltonian Models

In this paper, the monodromy variant of Newton’s method is applied to locate periodic or quasi-periodic relative satellite motion. Advantages of using Newton’s method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, ability to deal with nonlinear dynamics, repeatability of the solutions due to its non-random nature, and fast convergence. A nonlinear Hamiltonian model is derived which incorporates eccentricity of the reference orbit, nonlinear gravitational terms and the J2 perturbation. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.