Sampled-data representation for relative motion along elliptical orbits

This paper concerns with the dynamics of TH equations both in the time domain and in the true anomaly domain. Based on the homogeneous solutions of TH equations, a state transition matrix for the TH equations in the true anomaly domain is obtained. The state transition matrix applies to any eccentric orbit. Through the state transition matrix, the sampleddata descriptions are obtained for both the TH equations and the dimensionless equations. In order to evaluate the sampleddata description presented in this paper, a discrete time model constructed by the state transition matrix derived by Melton is introduced. At last simulations present the errors between these sampled-data descriptions.