DYNAMICAL BEHAVIOUR OF COMPRESSIBLE HOMOGENEOUS UNIFORMLY ROTATING ELLIPSOIDS WITH NONPARALLEL ANGULAR VELOCITY AND VORTICITY

Abstract

The study of nonequilibrium, self-gravitating, compressible, homogeneous and uniformly rotating gaseous ellipsoidal models is extended from parallel to nonparallel angular velocity and vorticity. The differential equations of motion governing these models are numerically integrated over ranges of initial values of angular velocity and vorticity. The dynamical behaviour of the ellipsoid is found to be almost unchanged when the initial values of Ω3/Ω3,e and λ3/λ3,e are interchanged, where λ is a function of the vorticity, Ω3 is the angular velocity along the x3 axis, and Ω3,e and λ3,e are equilibrium values. Models with the same initial value of | Ω3/Ω3,e - λ3/λ3,e | have similar dynamical behaviour. When this value becomes larger, the oscillations of the semi-axes are larger and are more nonperiodic. For all models, the ellipsoidal configuration is maintained at all times. The magnitude of Ωl depends on the difference between the values of the semi-axes am and an, where l, m, and n are cyclic. The smaller this difference is, the larger the angular velocity along the third axis. Thus whenever the model approaches a spheroidal configuration, there may be a large and rapid increase in the angular velocity along the axis of ‘symmetry’. The last two properties, namely the maintenance of the ellipsoidal configuration and the large increase in angular velocity of the model, configuration also hold in the model (T.T.Chia and S.Y.Pung, 1995, Astrophys.\ Space Sci., 229, 215.) with parallel angular velocity and vorticity. However, unlike the earlier model, Ω2 and Ω3 are observed to reverse their directions at certain instants during the oscillations; this may have interesting astrophysical implications.