GAUSSIAN ELEMENT FORMULATION OF SHORT-AXIS-MODE ROTATION OF A RIGID BODY

Abstract

Equations of the short-axis-mode rotation of a rigid body under a general torque field are derived in terms of a new set of variables. The transformation between the new variables and the non-canonical Andoyer variables is explicitly given in closed form. The right-hand sides of the new equations are the sum of two main terms for two angle variables and six perturbative terms. All the perturbative terms are expressed as linear combinations of torque vector components. In the case of torque-free motions, the two angle variables become linear functions of time and the remaining four variables become constants of motion. As a result, the new variables consist of a set of rotational elements in a broad sense. This formulation is a counterpart, in rotational dynamics, of the Gaussian formulation of the Keplerian orbital elements for elliptic orbits.