Mathematics
Scientific paper
May 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978apj...221..937f&link_type=abstract
Astrophysical Journal, Part 1, vol. 221, May 1, 1978, p. 937-957.
Mathematics
137
Euler-Lagrange Equation, Flow Stability, Newtonian Fluids, Nonrelativistic Mechanics, Perturbation Theory, Stellar Rotation, Angular Momentum, Canonical Forms, Displacement, Energy Conservation, Flow Equations, Gauge Invariance, Operators (Mathematics), Variational Principles
Scientific paper
The reported investigation is concerned with fluid perturbation theory and with the secular instability of rotating Newtonian stars. A formalism is developed for perturbations of a stationary Newtonian fluid, and a description is introduced of fluid perturbations in terms of a Lagrangian displacement. The class of trivial displacements is identified, and an explicit form is obtained for the generic trivial. The formal structure of the perturbation equations is considered. The canonical energy and angular momentum are introduced, together with two related dynamically conserved inner products. It is found that the canonical energy and angular momentum do not vanish on trivial displacements. An explicit relation is obtained between the canonical and physical conserved quantities. The inner products are used to characterize a dynamically invariant class of canonical displacements orthogonal to the trivials.
Friedman John L.
Schutz Bernard F.
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