An element formulation for perturbed motion about the center of mass

Abstract

The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements:l, the magnitude of the angular momentum vector;h, the total energy; τ and e, two linear functions of the independent variable; and ψ1 and θ1, two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body.