Linearized J2 and atmospheric drag model for satellite relative motion with small eccentricity

A new set of linearized differential equations governing relative motion between satellites in a formation is derived, taking into account the effects of J2 as well as atmospheric drag. This set of equations is more convenient than the corresponding nonlinear equations for designing formation control system or for implementing guidance algorithms. It is assumed that the eccentricity of the chief's orbit is small. In addition, the corresponding constant linearized equations are also proposed without numerical integrated, which is more convenient for engineering applications. Simulations show that the results obtained from the linearized model are quite close to those obtained by integrating the nonlinear dynamics model.