Relative spacecraft motion: A hamiltonian approach to eccentricity perturbations

This paper uses a Hamiltonian approach to find the effects of eccentricity perturbations on the linearized relative motion of spacecrafts described by Hill's equations. Perturbations to the constant canonical elements, obtained by a Hamiltonian treatment of the linearized relative motion, are considered. To begin with, the relative motion is described in an eccentric reference frame. Subsequently, the perturbing Hamiltonian is found in terms of the eccentricity. Next, a perturbation analysis is carried out via a variation of parameters procedure, generating a closed-form solution for variations about the eccentric reference orbit. Finally, using the orbit-averaged equations, the eccentricity effects on boundedness are discussed.