The Structure, Stability, and Dynamics
of Self-Gravitating Systems

Joel E. Tohline
tohline@rouge.phys.lsu.edu

uestion:

The equation of continuity [I.B.3] and the first law of thermodynamics [I.C.14] both can be written in the following "conservative" forms:

where q is a scalar physical variable. What does the variable q represent in the case of the equation of continuity? What does it represent in the case of the first law of thermodynamics?

Show that by setting ¶_t ® 0 and imposing simple rotation, the left-hand-side of this equation automatically goes to zero for any axisymmetric functional form of the variable q.

nswer:

uestion:

Assuming that H = 0 at r = 0, show that the analytical expression for the enthalpy H(r) of a polytropic gas is,

nswer:

uestion:

Show that the centrifugal potential y(v) for any object that is rotating uniformly with angular velocity W_o is,

if h_o = W_o.

nswer:

Go to Structure Chapter-Axisymmetrical Systems Answers Page 2

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Click in the table below to see homework solutions from other chapters.

Context Principal Governing PDE's Supplemental Relations

Applications Structure Spherical Axisymmetrical Nonaxisymmetrical HSCF Code Stability Dynamics

Appendices Mathematical Operators Integrals of the Motion

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