Modeling and analysis of dynamics for spacecraft relative motion actuated by inter-satellite non-contacting force

With the recent flurry of research on spacecraft relative motion actuated by inter-satellite non-contacting force, i.e., electrostatic force, electromagnetic force and magnetic flux-pinned force, the need has become apparent for dynamic modeling and dynamics analysis that capture the characteristics of this generic force. Based on the basic derivation of electrostatic force model and some theorems, the actuations of electrostatic force, electromagnetic force/torque and magnetic flux-pinned force/torque are unified and the corresponding mathematic models are derived. And then, with a general notation of this inter-satellite non-contacting force, the dynamic models are developed with respect to several assumptions of circular orbit, elliptical orbit and general Keplerian orbit pertaining to the motion of center of mass of the spacecraft cluster. A detailed dynamics analysis based on these derived models are carried out, including constraints of the relative motion dynamics, the special characteristics of applications to the near-Earth relative orbit motion and the deep space relative motion, and then a case with co-rotating pair of satellites subject to the previously mentioned inter-satellite non-contacting forces was simulated to validate the dynamic modeling and dynamics analysis. At last, some useful conclusions follow.