The precession and nutation of deformable bodies

The aim of the present paper will be to derive from the fundamental equations of hydrodynamics the explicit form of the Eulerian equations which govern the motion about the centre of gravity of self-gravitating bodies, consisting of compressible fluid of arbitrary viscosity, in an arbitrary external field of force. If the problem is particularized so that the external field of force represents the attaction of the sun and the moon, this motion would represent the luni-solar precession and nutation of a fluid viscous earth; if, on the other hand, the external field of force were governed by the earth (and the sun), the motion would define the physical librations of the moon regarded as a deformable body. The same equations are, moreover, equally applicable to the phenomena of precession and nutation of rotating fluid components in close binary systems, distorted by mutual tidal action; and the present paper contains the first formulation of the effects of viscosity on such phenomena.Investigation supported in part by the U.S. National Aeronautics and Space Administration under Contract No. NASW-1470.