Semianalytical Technique for Six-Degree-of-Freedom Space Object Propagation

Abstract

The cannonball assumption of three-degree-of-freedom (3DOF) space object state prediction can lead to large inaccuracies if the sphericity assumption is violated, while numerical propagation of both the translational and rotational (6DOF) equations of motion is computationally expensive. In this paper, a middle ground is proposed, in which the translational equations of motion are propagated numerically using approximate attitude predictions obtained via a closed-form perturbation solution. The capabilities of this semianalytical “hybrid” of special and general perturbation techniques are illustrated using a specific attitude solution, which assumes a fast-rotating, triaxial rigid body in an elliptical orbit subject to gravity-gradient torque. Even when these assumptions are mildly violated—such as when modeling higher-fidelity forces and torques—the approximate attitude predictions allow for more accurate modeling of body forces than a 3DOF cannonball propagation. In numerical examples in which attitude-dependent dynamics are considered, the hybrid method produces position predictions one or more orders of magnitude more accurate than a 3DOF cannonball propagation while requiring approximately one-third of the CPU time of a full 6DOF propagation for certain accuracy tolerance levels. Relative speedups achievable by the hybrid method are shown to increase as the rotation rate of the body increases.