Seminar 25th January 2012 2 p.m. University of Southampton, Building 13 (Tizard) Room 3019
A Search for Invariant Relative Satellite Motion
Dr Victor M Becerra
University of Reading
- Submitter
- Petrina Butler
The need to minimise fuel consumption in formation flying spacecraft has motivated significant research aimed at improving our understanding of the long term relative motion of satellites. A classical method for analysing the relative motion of satellites was proposed by Clohessy and Wiltshire in the 1960s , who linearised the two body problem about a circular orbit and solved the resulting linear system. It should be noted that dynamic modelling deficiencies will lead to unexpected relative satellite motion, while any inaccuracy in the prediction of the motion will lead to unnecessary maneuvering to eliminate possibly benign perturbations.
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. Principal Component Analysis (PCA) is applied to the resulting quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. Closed-loop control of relative satellite motion is simulated with the aid of a discrete LQR controller with impulsive actuation.