Rotational dynamics of deformable celestial bodies

Abstract

In a previous paper of this series (Tokis, 1973b) the Eulerian differential equations, which govern three-dimensional rotation of celestial bodies consisting of fluid material, have been set up with special respect to a description of effects of viscous friction exhibited in a binary system consisting of a close pair of such bodies. In order to study their solution, in the present investigation we shall depart from one differential equation which governs the simple rotation about an axis perpendicular to the orbital plane of the system.

A solution of this differential equation is given using modified Bessel functions for the case of constant orbital elements. This solution simplifies matters for the Earth-Moon system (or other similar systems). Methods are discussed for numerical integration of this equation, when the rotating body is spherical, with constant viscosity at the surface of the body, or spheroidal with constant viscosity throughout the whole body; these methods have been extended to the case in which the orbital elements of the system are given very approximately by explicit functions of the time.