Lagrangian invariants in the equilibrium conditions of an ideal rotating fluid
Abstract
It is shown that the velocity distribution and equilibrium conditions of the selfgravitating configurations from an ideal fluid are closely related with the presence of freezingin vector fields determined by means of scalar potentials, whose total derivative is equal to zero. Ignorance of integrals of motion connected with the existence of freezingin fields did not allow one to obtain the complete equilibrium conditions by variational method and, especially, led to the divergence in Lyapunov's and Riemann's results. This defect is eliminated in the paper and the equilibrium conditions and velocity distribution are considered by a single approach in the models of: (1) homogeneous fluid; (2) compressible fluid; (3) fluid with a magnetic field; (4) ideal fluid in the PNA of GR.
 Publication:

Astrophysics and Space Science
 Pub Date:
 June 1991
 DOI:
 10.1007/BF00644226
 Bibcode:
 1991Ap&SS.180...19K
 Keywords:

 Ideal Fluids;
 Lagrangian Equilibrium Points;
 Relativity;
 Rotating Fluids;
 Thermodynamic Equilibrium;
 Barotropic Flow;
 Compressible Fluids;
 Integral Equations;
 Liapunov Functions;
 Magnetic Fields;
 Thermodynamics and Statistical Physics