Nonlinear reduced order dynamics of spacecraft relative motion for a circular chief orbit

Nonlinear reduced order models are obtained for spacecraft relative motion in the case of circular chief orbits. First, a nonlinear third order extension of the CWH equations is obtained and a modal transformation is employed that decouples the linear dynamics. Then two techniques, linear-based order reduction and the methodology of nonlinear normal modes, are employed to obtain nonlinear reduced models corresponding to the three modes of the CWH equations. The resulting nonlinear models extend linear modal analysis of the CWH equations to the nonlinear regime valid for larger separation distances and allow for a geometric characterization of the nonlinear dynamics of relative motion.