22
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

The dynamics of isocirculational flows

&
Pages 1-33 | Received 29 Jan 1985, Published online: 01 Dec 2006

References

  • Arnold , V. I. 1966a . Sur un principe variationnel pour les écoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilite non linéaires . J. Méch. , 5 : 29
  • Arnold , V. I. 1966b . Sur la géometric differentielle des Groupes de Lie de dimension infinie et ses applications a 1′hydrodynamique des fluides parfaits . Ann. Inst. Fourier Grenoble , 16 : 319
  • Arnold , V. I. 1978 . Mathematical Methods of Classical Mechanics , Berlin : Springer Verlag . Appendix 5
  • Chandrasekhar , S. 1969 . Ellipsoidal Figures of Equilibrium , 64 Yale University Press .
  • Däppen , W. 1984 . “ Nonlinear nonradial adiabatic stellar oscillations: Numerical results for many-mode couplings ” . In Proc. 25th Liege Int. Astroph. Colloq. , 474 Université de Liège .
  • Däppen , W. and Perdang , J. Solar oscillations: The challenge of non-linearity . Proc. European Phys. Soc. Soc. Study Conference on Oscillations as a Probe of the Sun's Interior . 1983 , Catania. Memorie della Societa Astronomica Italiana . (in press)
  • Ertel , H. 1942 . Ein neuer hydrodynamischer Wirbelsatz . Meteorol. Zeit. , 59 : 277
  • Friedman , J. L. and Schutz , B. F. 1978 . Lagrangian perturbation theory of non-relativistic fluids . Astrophys. J. , 221 : 937
  • Friedman , J. L. and Schutz , B. F. 1978 . Secular instability of rotating Newtonian stars . Astrophys. J. , 222 : 281
  • Grinfeld , M. A. 1984 . Variational principles and stability of stationary flows of barotropic ideal fluid . Geophys & Astrophys. Fluid Dyn. , 28 : 31
  • Herivel , J. W. 1955 . The derivation of the equations of motion of an ideal fluid by Hamilton's Principle . Proc. Comb. Philos. Soc. , 51 : 344
  • Katz , J. and Lynden-Bell , D. 1982 . A Lagrangian for Eulerian fluid mechanics . Proc. R. Soc. London A , 381 : 263
  • Katz , J. 1984 . “ Most effective potentials for stability analysis ” . In Proc. 25th Liège Int. Astrophys. Colloq. , 420 Université de Liège .
  • Lanczos , C. 1975 . The Variational Principles of Mechanics , 4th edition Toronto University Press . Appendix II
  • Lamb , H. 1945 . Hydrodynamics , 14 Dover Publ. .
  • Lebovitz , N. R. 1965 . “ The Riemann ellipsoids ” . In Lecture Notes Institut Astrophys. Cointe Sclessin , 29 Université de Liège .
  • Lebovitz , N. R. 1981 . On the fluid dynamics of evolving stars . Proc. R. Soc. London A , 375 : 249
  • Lebovitz , N. R. 1983 . On the fission theory of binary stars, III: The formulation of the bifurcation problem . Astrophys. J. , 275 : 316
  • Ledoux , P. 1958 . Stellar stability . Handbuch der Physik , 51 : 619
  • Lin , C. C. 1963 . “ Liquid helium ” . In Proc. Int. School Phys. XXI , Academic Press .
  • Lynden-Bell , D. and Katz , J. 1981 . Isocirculational flows and their Lagrangian and energy principles . Proc. R. Soc. London A , 378 : 179
  • Marsden , J. and Weinstein , A. 1974 . Reduction of symplectic manifolds with symmetry . Rep. Math. Phys. , 5 : 121
  • Mittag , L. , Stephen , N. J. and Yourgrau , W. 1968 . “ Variational principles in hydrodynamics ” . In Variational Principles in Dynamics and Quantum Theory , 2nd Edition Edited by: Yourgrau , W. and Mandelstam , S. 142 London : Pitman and Son .
  • Mobbs , S. D. 1982 . Variational principles for perfect and dissipative fluid flows . Proc. R. Soc. London A , 381 : 457
  • Seliger , R. L. and Whitham , G. B. 1968 . Variational principles in continuum mechanics . Proc. R. Soc. London A , 305 : 1
  • Serrin , J. 1959 . Mathematical principles of classical fluid mechanics . Handbuch der Physik , 8 : 148
  • Whittaker , E. T. 1937 . A Treatise on the Analytical Dynamics of Particles and Rigid Bodies , 341 Cambridge University Press .
  • Yang , C. N. and Mills , R. L. 1954 . Conservation of isotopic spin and isotopic gauge invariance . Phys. Rev. , 96 : 191

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.