Abstract
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.
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References
Bardeen, J.M.: 1975, in: A. Hayli (ed.),Dynamics of Stellar Systems, IAU Symp.69, D. Reidel Publ. Co., Dordrecht, The Netherlands, p. 297.
Binney, J. and Tremaine, S.: 1987, Galactic Dynamics,Princeton Series in Astrophysics, Princeton University Press, Princeton, New Jersey.
Black, D. and Bodenheimer, P.: 1975,Astrophys. J. 199, 619.
Chandrasekhar, S.: 1987,Ellipsoidal Figures of Equilibrium, Dover Publications, Inc., New York.
Contopoulos, G., Papadaki, H. and Polymilis, C.: 1994,Celes. Mech. 60, 249.
Cox, J.P.: 1980,Theory of Stellar Pulsation, Princeton University Press, Princeton, New Jersey.
Dirichlet, G.L.: 1860,J. Reine Angew. Math. 58, 217.
Durisen, R.H.: 1978,Astrophys. J. 224, 826.
Durisen, R.H. and Bacon, D.A.: 1981,Astrophys. J. 245, 829.
Fujimoto, M.: 1968,Astrophys. J. 152, 523.
Gear, C.W.: 1971,Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey.
Gustavson, F.G.: 1966,Astrophys. J. 71, 670.
Heiskanen, W.A.: 1957,Transactions of the American Geophysical Union 38, 238.
Hénon, M. and Heiles, C.: 1964,Astrophys. J. 69, 73.
Hunter, C.: 1972,Ann. Rev. Fluid. Mech. 4, 219.
Jeffreys, H.: 1959,The Earth, Cambridge University Press, Cambridge.
Lau, Y.T., Finn, J.M and Ott, E.: 1991,Phys. Rev. Letters 66, 978.
Lebovitz, N.R.: 1961,Astrophys. J. 134, 500.
Lebovitz, N.R.: 1967,Ann. Rev. Astron. Astrophys. 5, 465.
Lebovitz, N.R.: 1983,Astrophys. J. 275, 316.
Lebovitz, N.R.: 1984,Astrophys. J. 284, 364.
Lyttleton, R.A.: 1953,Theory of Rotating Fluid Masses, Cambridge University Press, Cambridge.
Press, W.H., Flannery, B.P. and Teukolsky, S.A.et al.: 1989,Numerical Recipes, The Art of the Scientific Computing, Cambridge University Press, Cambridge.
Rosensteel, G. and Tran, H.Q.: 1991,Astrophys. J. 366, 30.
Rossner, W.: 1967,Astrophys. J. 149, 145.
Takahara, F.: 1976,Prog. Theor. Phys. Kyoto 56, 1665.
Tassoul, J.L.: 1978,Theory of Rotating Stars, Princeton University Press, Princeton, New Jersey.
Toomre, A.: 1977,Ann. Rev. Astron. Astrophys. 15, 437.
Watanabe, T. and Inagaki, S.: 1992,Publ. Astron. Soc. Japan 44, 561.
Weber, S.V.: 1976,Astrophys. J. 208, 113.
White, S. and Silk, J.: 1979,Astrophys. J. 231, 1.
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Brunini, A., Giordano, C.M. & Plastino, A.R. Numerical exploration of the dynamics of Self-Adjoint S-Type Riemann ellipsoids. Astrophys Space Sci 234, 153–167 (1995). https://doi.org/10.1007/BF00627289
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DOI: https://doi.org/10.1007/BF00627289