A Full-Body Relative Orbital Motion of Spacecraft Using Dual Tensor Algebra and Dual Quaternions

This paper proposes a new non-linear differential equation for the six degrees of freedom (6-DOF) relative rigid bodies motion. A representation theorem is provided 6-DOF motion in arbitrary non-inertial reference frame. The problem two spacecraft specific case Keplerian confocal orbits proposed. result an analytical method without secular terms and singularities. Tensors dual algebra quaternions play fundamental role, with solution being problem. Furthermore, theorems rotation translation parts orbital problems are obtained.