Revision as of 17:38, 21 March 2010

Preface from the original version of this HyperText Book (H_Book):

November 18, 1994

Much of our present, basic understanding of the structure, stability, and dynamical evolution of individual stars, short-period binary star systems, and the gaseous disks that are associated with numerous types of stellar systems (including galaxies) is derived from an examination of the behavior of a specific set of coupled, partial differential equations. These equations — most of which also are heavily utilized in studies of continuum flows in terrestrial environments — are thought to govern the underlying physics of all macroscopic "fluid" systems in astronomy. Although relatively simple in form, they prove to be very rich in nature... <more>

Pictorial Table of Contents

Pictorial Table of Contents

Context

Principal Governing Equations
- Continuity Equation
- Euler Equation
  - Rotating Reference Frame
- <math>1^\mathrm{st}</math> Law of Thermodynamics
- Poisson Equation

Supplemental Relations
- Total Pressure
  - Quartic Temperature Solution

Virial Equations

Applications

Spherically Symmetric Configurations

Introduction

Structure:

Solution Strategies
Example Solutions:
- Uniform-density sphere
- Polytropes
- Zero-temperature White Dwarf
- Isothermal sphere

Stability:

Solution Strategy
Example Solutions:
- Uniform-density sphere
- Polytropes

Dynamics:

Appendices

@@ Line 19: / Line 19: @@
 =Context=
-:[http://www.vistrails.org/index.php/User:Tohline/PGE#Principal_Governing_Equations Principal Governing Equations]
+* [[User:Tohline/PGE#Principal_Governing_Equations|Principal Governing Equations]]
+** [[User:Tohline/PGE/ConservingMass#Continuity_Equation|Continuity Equation]]
+** [[User:Tohline/PGE/Euler#Euler_Equation|Euler Equation]]
+*** [[User:Tohline/PGE/RotatingFrame#Rotating_Reference_Frame|Rotating Reference Frame]]
+** <math>1^\mathrm{st}</math> Law of Thermodynamics
+** Poisson Equation
-:[http://www.vistrails.org/index.php/User:Tohline/SR Supplemental Relations]
+* [[User:Tohline/SR#Supplemental_Relations|Supplemental Relations]]
+** [[User:Tohline/SR/PressureCombinations#Total_Pressure|Total Pressure]]
+*** [[User:Tohline/SR/Ptot_QuarticSolution#Determining_Temperature_from_Density_and_Pressure|Quartic Temperature Solution]]
-:Virial Equations
+* Virial Equations
 =Applications=
 ==Spherically Symmetric Configurations==
-If the self-gravitating configuration that we wish to construct is spherically symmetric, then the coupled set of multidimensional, partial differential equations that serve as our [http://www.vistrails.org/index.php/User:Tohline/PGE principal governing equations] can be simplified to a coupled set of one-dimensional, ordinary differential equations.  This is accomplished by expressing each of the multidimensional spatial operators &#8212; gradient (<math>\nabla</math>), divergence (<math>\nabla\cdot</math>), and Laplacian (<math>\nabla^2</math>) &#8212; in spherical coordinates (<math>r, \theta, \varphi</math>) (see, for example, the [http://en.wikipedia.org/wiki/Spherical_coordinate_system#Integration_and_differentiation_in_spherical_coordinates Wikipedia discussion of integration and differentiation in spherical coordinates]) then setting to zero all derivatives that are taken with respect to the angular coordinates <math>\theta</math> and <math>\varphi</math>.  After making this simplification, our governing equations become... [http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/PGE <more>]
+[[User:Tohline/SphericallySymmetricConfigurations/PGE|Introduction]]
 ===Structure:===
-* <font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies Solution Strategies]'''</font>
+* <font color="darkblue">'''[[User:Tohline/SphericallySymmetricConfigurations/SolutionStrategies|Solution Strategies]]'''</font>
 * Example Solutions:
-** [http://www.vistrails.org/index.php?title=User:Tohline/SSC/UniformDensity Uniform-density sphere]
+** [[User:Tohline/SSC/UniformDensity|Uniform-density sphere]]
-** [http://www.vistrails.org/index.php/User:Tohline/SSC/Polytropes Polytropes]
+** [[User:Tohline/SSC/Polytropes|Polytropes]]
 ** Zero-temperature White Dwarf
 ** Isothermal sphere
@@ Line 42: / Line 49: @@
 ===Stability:===
-* <font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SSC/Perturbations Solution Strategy]'''</font>
+* <font color="darkblue">'''[[User:Tohline/SSC/Perturbations|Solution Strategy]]'''</font>
 * Example Solutions:
-** [http://www.vistrails.org/index.php?title=User:Tohline/SSC/UniformDensity Uniform-density sphere]
+** [[User:Tohline/SSC/UniformDensity|Uniform-density sphere]]
-** [http://www.vistrails.org/index.php/User:Tohline/SSC/Polytropes Polytropes]
+** [[User:Tohline/SSC/Polytropes|Polytropes]]
-===<font color="darkblue">'''[http://www.vistrails.org/index.php/User:Tohline/SphericallySymmetricConfigurations Dynamics]:'''</font>===
+===<font color="darkblue">'''[[User:Tohline/SphericallySymmetricConfigurations|Dynamics]]:'''</font>===
 =Appendices=
 {{LSU_HBook_footer}}

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