Joel2: /* Generalization */

2023-12-16T01:11:27Z

Generalization

← Older revision		Revision as of 21:11, 15 December 2023
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	[<b>[[Appendix/References#Shu92\|<font color="red">Shu92</font>]]</b>, Vol. II, pp. 329-330] <font color="orange">If we were to multiply [this modified Euler equation] by <math>~x_m</math> and integrate over volume <math>V</math>, we would get the [appropriately modified] ''tensor virial theorem'', the off-diagonal elements of which carry information concerning angular-momentum conservation (see </font>[<b>[[Appendix/References#EFE\|EFE]]</b>] <font color="orange">for an exposition). [Here] we shall be more interested in the trace of the tensor equation, which we may derive by simply multiplying [the modified Euler equation] by <math>~x_i</math> (with an implicit summation over repeated indices) and integrating over <math>V</math></font>. The resulting relation governing the equilibrium of stationary states (see [<b>[[Appendix/References#Shu92\|<font color="red">Shu92</font>]]</b>] for derivation details), as we shall reference it, is the		[<b>[[Appendix/References#Shu92\|<font color="red">Shu92</font>]]</b>, Vol. II, pp. 329-330] <font color="orange">If we were to multiply [this modified Euler equation] by <math>~x_m</math> and integrate over volume <math>V</math>, we would get the [appropriately modified] ''tensor virial theorem'', the off-diagonal elements of which carry information concerning angular-momentum conservation (see </font> [<b>[[Appendix/References#EFE\|<font color="red">EFE</font>]]</b>] <font color="orange">for an exposition). [Here] we shall be more interested in the trace of the tensor equation, which we may derive by simply multiplying [the modified Euler equation] by <math>~x_i</math> (with an implicit summation over repeated indices) and integrating over <math>V</math></font>. The resulting relation governing the equilibrium of stationary states (see [<b>[[Appendix/References#Shu92\|<font color="red">Shu92</font>]]</b>] for derivation details), as we shall reference it, is the
	<div align="center">		<div align="center">
	<span id="GenTVE"><font color="#770000">'''Generalized Scalar Virial Theorem'''</font></span><br />		<span id="GenTVE"><font color="#770000">'''Generalized Scalar Virial Theorem'''</font></span><br />

Joel2: Created page with "FORCETOC =Global Energy Considerations= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#9390DB;" | Global Energy
Considerations |} ==Preface== The astrophysics community relies heavi..."

2023-12-11T20:19:52Z

Created page with "__FORCETOC__   =Global Energy Considerations= {| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black" |- ! style="height: 125px; width: 125px; background-color:#9390DB;" | Global Energy Considerations |} ==Preface== The astrophysics community relies heavi..."

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Joel2: /* Generalization */