Solution of the gravitational polytrope equations by using the quasi-invariance group

Details Solution of the gravitational polytrope equations by using the quasi-invariance group Solution of the gravitational polytrope equations by using the quasi-invariance group

Dec 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982crasb.295..993b&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie II, Mecanique, Physique, Chimie, Sciences de l'Univers, Sciences de la Terr

Physics

1

Gravitation Theory, Hydrodynamic Equations, Invariance, Polytropic Processes, Stellar Evolution, Nonlinear Equations, Novae, Partial Differential Equations, Protostars, Stellar Models, Supernovae

Scientific paper

The nonlinear hydrodynamic equations are employed to model the dynamic evolution of a gaseous mass, with the quasi-invariance group used to obtain solutions. The model describes the formation of a star from a low density cold gaseous mass. The constitutive equations are the Euler, Poisson, continuity, and adiabatic motion equations. Techniques for deriving solutions of partial differential equations based on a dimensional analysis of invariant groups are demonstrated. The evolution of the gaseous mass starts from an initial velocity, and dual hydrostatic equilibrium is analytically defined, as is equilibrium within a field. A generalized Lane-Emden equation is formulated to indicate the correlation between the frequencies and spatial structure. The analysis is also applicable to novae and supernovae.

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