THE N-TH-ORDER VIRIAL THEORY - PERMITTED FIGURES OF EQUILIBRIUM

In the virial method we take moments of the equations of motion, from which we study the equilibrium and the stability of ellipsoidal figure s. The virial equations of the various orders given by Chandrasekhar ( Ellipsoidal Figures of Equilibrium, 2nd edition (Dover, New York, N.Y. ) 1987) in the case of homogeneous and uniformly rotating masses, are generalized to nonuniformly rotating ellipsoidal configurations of non homogeneous density, with internal fluid motions of nonuniform vortici ty. We derive the permitted equilibrium figures using the higher-order virial equations and we give a suitable classification.