Numerical Exploration of the Dynamics of Self-Adjoint S-Type Riemann Ellipsoids

BRUNINI, A.; GIORDANO C. M.; PLASTINO R. A.

ASTROPHYSICS AND SPACE SCIENCE

SPRINGER

Lugar: Berlin; Año: 1995 vol. 234 p. 153 - 167

0004-640X

A Riemann ellipsoid is a self-gravitating fluid whose velocity field is a linear function of the position coordinates. Though the theory of the equilibrium and stability is thoroughly developed, scarse attention has been paid to the dynamical behaviour. In this paper we present a numerical exploration of the phase-space structure for the Self-Adjoint S-Type Riemann ellipsoids via Poincaré surfaces of section, which reveal a rich and complex dynamical behaviour. Both the occurrence of chaos for certain values of the parameters of the system as well as the existence of periodic orbits are observed. We also considered ellipsoids embedded in rigid, homogeneous, spherical halos, obtaining evidence of the stabilizing effect of halos even in the case of finite-amplitude oscillations. Moreover, we show that the approximated equations of motion derived by Rosensteel and Tran (1991) fail to describe properly the phase-space structure of the problem.