Backing Trojan Asteroids in Periodic and Quasi-Periodic Orbits around the Jupiter Lagrange Points using LDV Techniques

Linear Dynamidly Varying (LDV) control is a technique for getting a natural (nonlinear, possibly chaotic) trajectory and a perturbed trajectory asymptotically synchroni7ed given an initial condition offset. Probably the best illustrative example, which motivates this paper, is tracking the natural (possibly quasi-periodic) molion of a Tkojan asteroid near the IA point of Jupiter with a spacecraft.that follows a trajectory perturbed by the non conservative propulsion forces. .The tracking error is linearized around the natural dynamics of the Trojan body, leading to an LDV niodel of the tracking error. This in turn leads to a dynamically varying c o n t r o h , itself given as the solution to a Partial Diffcrehial Riccati Equation, solved via the method of characteristics. It is shown that this technique dlows for ;xcura,te tracking of the coniplicated dynamics around the L4 point.