Talk:Virial theorem

message: I wonder who wrote this page, but I'd like to remind him that copyright should be respected.
If you compare this page with Goldstein's "Classical Mechanics" p.70, you'd understand my point.
Besides, if you intend to copy anyway, please state "if the force is central" just before "If V is a power-law function of r". This can't be omitted, because you are using the same r to represent the position vector and the radius vector ambiguously.
: I put a notice at Wikipedia:Copyright problems but I don't know the proper procedure for this. 80.203.45.67 14:00, 8 April 2006 (UTC)
replies: text: Which edition? Zarniwoot 00:20, 14 May 2006 (UTC)
thread_title:  Have you heard of Copyright? 

message: I don't like the nomenclature K for the kinetic energy. Remember that K is still often used for force, too, especially in Special Relativity, given that until the 40s, German was especially important in physics. In German, force is named Kraft and the relativistic 4-force is often written as K.
For the kinetic energy, the nomenclature KE (when not E(kin) or something like that) is much better. However, E would be very good to appear, since the official term for energy is E or W (of work). I think, an often used abbreviation for kinetic energy is T.
N.M.B.R.Nbez 11:06, 7 May 2006 (UTC)
thread_title:  Nomenclature 

message: I've reverted to the revision (cur) (last)  03:08, 6 May 2004 158.193.210.45, as per concerns raised above that this is a copyright violation of "Classical Mechanics". As I don't have a copy of the book, I'm unable to check what exactly is a copyright violation. 
Please see this for a list of differences between that version and the pre-copyright violation noted version. I've also restored the interwiki links as well as the external links to the version right before it was noted as a copyright violation. Jude (talk,contribs,email) 03:10, 15 May 2006 (UTC)
thread_title:  Copyvio 

message: Hi all, I re-wrote this article from scratch without looking at any outside sources (e.g., books, articles or websites), so there should be no copyright problem now.  I did keep the G notation for the virial, but that's about the only hold-over.  I'm clueless about how the virial theorem has been used in other settings (e.g., for gases or in quantum mechanics), though, so I'm looking forward to your additions! :D  WillowW 10:51, 9 July 2006 (UTC)
thread_title: No copyvio; have fun!

message: Something about its significance? —Preceding unsigned comment added by HairyDan (talk • contribs) 22:08, 17 October 2006 (UTC)
replies: text: I made an try at this; does it seem good to you? Willow 23:06, 17 October 2006 (UTC)
thread_title:  Intro needed? 

message: This not exactly a technical issue, but for precision's sake...
Although "virial" actually comes from "vis" (force, strength), the Latin substantive is highly irregular, and the genitive form is "roboris" (which was a genitive borrowed, quite curiously, from "robur, roboris", oak). The quoted genitive "viris" doesn't actually exist, and "roboris" would only be confusing... I have simply deleted the genitive.
Massimo 10:43, 18 December 2006 (UTC)
replies: text: Wow, that's a surprise — thanks for catching that!  I knew that vis was irregular in some cases (e.g., vim and vi) but I had so often read the nominative plural vires that I just assumed that there was a corresponding genitive singular. :(  Thanks very much, Massimo; I love the way Wikipedia helps us to help each other and learn new things from each other. :)  Warm wishes for the holidays,  Willow (a distant relative of Quercus robur ;) 15:31, 18 December 2006 (UTC)
thread_title:  A little mistake in the etymology 

message: In the section on the virial radius formula, "H" and "G" should be defined immediately before or after the formula. I'd do it myself, but I'm not sure what H is! A reference would also be good...perhaps one of the "references" or "additional readings" already listed would work? Finally, it could use a sentence giving some context as to why the virial radius is defined the way it is, and why it's a useful thing to think about (for example, is the factor of 200 arbitrary?) Steve 15:05, 16 July 2007 (UTC)
replies: text: I tried to fix it some, e.g. indicating that the factor 200 is arbitrary, but I find this section rather suspect nonetheless. --Art Carlson 20:45, 18 July 2007 (UTC)
thread_title:  Virial radius 

message: This is a great article, but how about a little more history?  It says Clausius gave the virial theorem it's definition.  Does this mean he originated it?  Proved it?  If not, who did?  --Chetvorno 07:48, 21 August 2007 (UTC)
replies: text: Yes, Claudius originated it, i.e. he derived it and presented in the form used in this article.--Zinger (talk) 11:53, 3 May 2010 (UTC)
thread_title: Who proved the virial theorem?

message: I believe that the statement 2 \langle T \rangle = n \langle V_{TOT} \rangle in the beginning, where  V_{TOT}  is said to be total potential energy of the system, to be correct the subscript of  V_{TOT} should be  V_{n} so that  n \langle V_{n} \rangle = \langle V_{TOT} \rangle. Thus making  \langle V_{n} \rangle the time average potential energy of the particle n, and the sum of all such particles in the system equal to  \langle V_{TOT} \rangle, the total time averaged potential energy of the system.
If someone could verify this to be true as well, it would be greatly appreciated.
Basilf1 (talk) 18:50, 13 May 2008 (UTC)
replies: text: Here n is not a number of particles but the power of distance in the expression for potential: 
V(r_{jk}) = \alpha r_{jk}^n,
. And V_{TOT} represents the net potential energy of the system. So the equation 2 \langle T \rangle = n \langle V_{TOT} \rangle is correct. --Zinger (talk) 17:21, 3 May 2010 (UTC)
thread_title: <math>n \langle V_{TOT} \rangle = \langle V_{TOT} \rangle</math>?

message: The article currently reads, "The scalar virial G  is defined by the equation
G = \sum_{k=1}^N \mathbf{p}_k \cdot \mathbf{r}_k
 ...". Subsequent parts of the derivations make references like "time derivative of the virial" which, from context, are consistent with calling this G the virial.
However, I'm more familiar with the virial being defined as something like -\frac{1}{2}\sum_{k=1}^N \left\langle \mathbf{F}_k \cdot \mathbf{r}_k \right\rangle
, or perhaps without the \frac{1}{2}, and maybe sometimes without the minus sign. Goldstein and and Thornton/Marion agree with thid  F\cdot r version. (I think T/M is just quoting Goldstein.) Landau/Lifshitz also agrees, but doesn't have the 1/2 in front. I'm not aware of any texts that define the virial in the p\cdot r way we're using here. Can anyone find a reference? I haven't seen Clausis's original work myself. 
I think the L/L and Goldstein references alone are sufficient to justify adding a sentence to the lead as, 
"... technical definition by Clausius in 1870. Modern usage varies by author as to which quantity in the virial theorem is known as "the virial" . Common choices include -\frac{1}{2}\sum_{k=1}^N \left\langle \mathbf{F}_k \cdot \mathbf{r}_k \right\rangle  and 2 times this quantity."
(with references to Goldstein and L/L as commonly accepted standards. 
If someone can quote a source with the p\cdot r version, that should be mentioned here, too.)
But, then the derivations would have to be cleaned up to be consistent with the F\cdot r virial instead of the current G. So, I thought I'd check for consensus before making that more extensive edit. (New editor here, please don't bite.)
Spatrick99 (talk) 21:01, 2 March 2010 (UTC)
replies: text: I've checked the sources on the definition of virial and your statement seems to be correct: virial should be defined like -\frac{1}{2}\sum_{k=1}^N \left\langle \mathbf{F}_k \cdot \mathbf{r}_k \right\rangle
. The only mentioning of the virial in the form 
G = \sum_{k=1}^N \mathbf{p}_k \cdot \mathbf{r}_k
 could be found on the page which link is located above in the discussion: John Baez's explanation of virial. But the author uses Goldstein as a reference, where virial is explicitly defined as the former. So, I agree on changing the definition. But that should not lead to any changes in the rest of the text (except where G is mentioned as a virial). Virial theorem could be proven even without introducing "virial" at all. --Zinger (talk) 12:52, 3 May 2010 (UTC)
thread_title:  Definition of the virial 

message: I think the article isn't clear enough on it.88.159.72.240 (talk) 01:00, 8 March 2010 (UTC)
thread_title:  '''Why''' <math>\left\langle \frac{dG}{dt} \right\rangle_\tau = 0</math> 

message: The article defines a scalar moment of inertia before defining the virial, but doesn't establish any meaningful connection between the two.  Should the use of the moment of inertia be removed?  If not, can it be better justified as a related idea?  70.247.169.94 (talk) 02:19, 4 July 2010 (UTC)
replies: text: Sure it does. The third equation in Section "Definitions of the virial and its time derivative" relates the two quantities, and the section "Inclusion of electromagnetic fields" discusses the relationship in the text as well. --Art Carlson (talk) 19:32, 4 July 2010 (UTC)
thread_title:  Why is moment of inertia introduced? 

message: From the Virial theorem, an average temperature for a star can be derived. From this, the stellar evolution can be predicted, from the expansion of a main sequence star as hydrogen is depleted up until after helium burning stops. 
I think it'd be a good idea to include something on this, and I'd write it myself except I don't know enough about it to be what you'd consider an accurate source. I can't find much literature on this on the internet, but it was something we did in my Astrophysics course, and it'd be a good application of the theorem to be included in the article.  — Preceding unsigned comment added by 31.205.74.33 (talk) 21:47, 24 May 2012 (UTC)
replies: text: I agree.  I'll try to add a section on 'Virial Theorem in Astrophysics' which will be a bit more general --- but still easily applied to stellar evolution. All Clues Key (talk) 15:40, 12 October 2012 (UTC)
thread_title:  Relevance to Stellar Evolution 

message: Substituted at 10:02, 30 April 2016 (UTC)
thread_title: Assessment comment