- Two analytical developments for the arbitrarily torqued motion of an asymmetric rigid body, both of which utilize a new torque-free solution as the reference motion, are presented. The first is an Encke-type perturbation formulation in which differential equations for the angular velocity and orientation departures from Poinsot motion are derived. The second technique is a variation of parameters scheme in which an analogue of Herrick's two-body perturbative differentiation technique is employed. The torque-free motion constants selected for variation are initial orientation and initial angular velocity; differential equations which specify the time variation of these parameters are developed, so that the torque-free solution is then instantaneously valid in the presence of arbitrary torques. Both developments are motivated by classical perturbation theories in orbital mechanics. Extensive use is made of the Euler parameter description of body orientation and kinematics rather than the more conventional Euler angles in order to avoid the geometrical singularities implicit in the latter. 1976 D. Reidel Publishing Company.