Rotational dynamics of a deformable medium: Further generalization

Abstract

Cauchy's fundamental first law of continuum mechanics is integrated over the whole mass of a self-gravitating deformable finite material continuum, viscolinear (i.e., Newtonian), not necessarily constrained to obey Stokes's condition, with viscosity coefficients given as arbitrary functions of the coordinates. The general Eulerian equation is derived, governing generalized rotation on which certain other cooperating deformations are superimposed. Finally, the explicit form of this equation is given for the case of a viscous gaseous polytrope.