Analytical Expansions of TorqueFree Motions for Short and Long Axis Modes
Abstract
Torquefree motion of a rigid body is integrable and its solution is expressed in terms of elliptic functions and elliptic integrals. The conventional analytical expression of the solution, however, is complicated and not suitable for handcalculation. Recently the rotational motions of small celestial bodies in the solar system are frequently investigated by numerically integrating the equations of motion instead of using the analytical solution, since the numerical evaluation of the analytical and exact solution is a little bit difficult. As the observational accuracy of the rotational motions of the small bodies in the solar system is quite low, what we need for the reduction of these observations are rough estimates of the period of Eulerian motion ( or the free precession period) and the amplitudes of the main periodic terms. Here we give simple analytical expansions of torquefree motions for short and longaxis modes, which are correct up to the secondorder of a small parameter. These expressions include only trigonometric functions and are easily evaluated by hand calculation for estimates of the essential quantities from which we can determine a global rotational motion of the torquefree motion. They can also be used as the zeroth order solution in a perturbation method, when the motion is perturbed by external torques.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 December 1992
 DOI:
 10.1007/BF00051817
 Bibcode:
 1992CeMDA..53..365K
 Keywords:

 Celestial Mechanics;
 Rigid Structures;
 Rotation;
 Solar System;
 Angular Momentum;
 Elliptic Functions;
 Numerical Integration;
 Torque;
 Astrophysics;
 Torquefree motionAndoyer variables