Il Nuovo Cimento B (1971-1996)

, Volume 105, Issue 8–9, pp 1047–1054 | Cite as

Nonlinear velocities in generalized riemann ellipsoids

  • S. Filippi
  • R. Ruffini
  • A. Sepulveda


The Dirichlet problem concerning the equilibrium conditions, under which a self-gravitating homogeneous fluid-mass can maintain at every instant an ellipsoidal form, is here generalized. We provide the conditions necessary to solve the Dirichlet problem in a more general case of heterogeneous masses having nonlinear internal motions, using the second-order virial equations. The conditions for the stability are presented. It is also proved that the Dedekind theorem generalized to these new solutions is valid. These models may lead to a direct explanation of some basic features of galactic morphology.


95.30 Fundamental aspects of astrophysics 


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  1. [1]
    C. G. J. Jacobi:Poggendorff Annalen der Physik und Chemie,33, 229 (1834).ADSCrossRefGoogle Scholar
  2. [2]
    G. Dirichlet:J. Reine Angew. Math.,58, 181 (1860).Google Scholar
  3. [3]
    R. Dedekind:J. Reine Angew. Math.,58, 217 (1860).MathSciNetGoogle Scholar
  4. [4]
    B. Riemann:Abh. Konigl. Gesell. Wis. zu Gottigen,9, 3 (1860).Google Scholar
  5. [5]
    S. Chandrasekhar:Ellipsoidal Figures of Equilibrium (Yale University Press, New Haven and London, 1969).MATHGoogle Scholar
  6. [6]
    S. Filippi, R. Ruffini andA. Sepulveda:Astron. Astrophys.,231, 30 (1990).MathSciNetADSMATHGoogle Scholar
  7. [7]
    S. Filippi, R. Ruffini andA. Sepulveda: in preparation (1990).Google Scholar
  8. [8]
    F. Pacheco, G. Pucacco andR. Ruffini:Astron. Astrophys.,161, 39 (1986).ADSMATHGoogle Scholar
  9. [9]
    G. Busarello, S. Filippi andR. Ruffini:Astron. Astrophys.,197, 91 (1988).ADSMATHGoogle Scholar
  10. [10]
    G. Busarello, S. Filippi andR. Ruffini:Astron. Astrophys.,213, 80 (1989).ADSGoogle Scholar
  11. [11]
    G. Busarello, S. Filippi andR. Ruffini:Astron. Astrophys.,227, 30 (1990).MathSciNetADSGoogle Scholar
  12. [12]
    F. Pacheco, G. Pucacco, R. Ruffini andG. Sebastiani:Astron. Astrophys.,210, 42 (1989).MathSciNetADSMATHGoogle Scholar
  13. [13]
    R. Wiegandt:Astron. Astrophys.,106, 240 (1982).ADSMATHGoogle Scholar

Copyright information

© Società Italiana di Fisica 1990

Authors and Affiliations

  • S. Filippi
    • 1
  • R. Ruffini
    • 1
  • A. Sepulveda
    • 1
  1. 1.ICRA, International Center for Relativistic Astrophysics Dipartimento di FisicaUniversitd di Roma I «La Sapienza»Roma

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