User talk:Jaycall

Joel's First Talk Message to Jay

Jay: In the email message that you sent to me today, you indicated that you had added the 3rd component to the dx/dt equation. I don't see that modification in the current T3Coordinates page. --Tohline 15:05, 29 May 2010 (MDT)

Joel: It's at the bottom of the section entitled "Time-Derivative of Position and Velocity Vectors". Under the history tab, can you see the edits that I made? It was the very first edit and was fairly minor. I only added a couple terms. --Jaycall 20:17, 29 May 2010 (MDT)

The mediaWiki "talk" page recommends that when you reply to a query, you should not start a new subsection but, rather, just indent (using one or more colons) immediately following the query. Also, it recommends that you "sign" each "talk" message. You do this by typing 2 dashes followed by 4 tildes! I'm going to edit your "reply" (and this additional one from me) to put it in this recommended format. But you have to "sign" your own remark. --Tohline 16:23, 29 May 2010 (MDT)

By the way, I can see the edits that you made to add the 3rd component to the dx/dt equation. I did not spot the changes earlier, but via the history "diff" function, I'm able to see the edits clearly. --Tohline 16:41, 29 May 2010 (MDT)

Killing Vector Approach

Thanks for writing out all the terms in the expression for <math>d\Xi/dt</math> in your "Killing Vector Approach" discussion. On the one hand, I'm happy that the term I mentioned cancels with another one because that means we have fewer terms to integrate. On the other hand, it was one term that I thought we might actually be able to manipulate analytically. Of the two terms that remain, one is relatively simple — the one that is proportional to <math>\dot{\lambda}_2</math> — but the first term is a bear! That will take some thinking! --Tohline 10:50, 30 May 2010 (MDT)

I know it seems like the wrong direction, but unless we can express this summary integral entirely in terms of <math>\lambda_1</math>, <math>\lambda_2</math>, <math>\dot{\lambda}_1</math> and <math>\dot{\lambda}_2</math>, I think that in order to make progress we're going to have to write things out in terms of <math>\varpi</math>, <math>z</math>, <math>\dot{\varpi}</math> and <math>\dot{z}</math>. Of course, that will make the expression much messier, but I think it will be very difficult to recognize this quantity as an exact derivative unless everything's in terms of the same coordinates. --Jaycall 12:55, 30 May 2010 (MDT)

I agree. It is for similar reasons that I am planning on focusing on the case where <math>q^2=2</math>. At least in this special case we can invert the coordinate expressions to give <math>\varpi</math> and <math>z</math> in terms of the <math>\lambda</math>s. Incidentally, I have added a link to your "Killing Vector" page as well as a link to this associated "Talk" page on the page where I itemize my various "ramblings". --Tohline 16:16, 30 May 2010 (MDT)

Good point. That would be a good reason to focus on one specific case. I haven't looked closely at the inverted coordinate transformation for the <math>q^2=2</math> case for several days. Since the relation is quadratic, is it obvious which root should be used?

The proper physical root was obvious to me when I performed the coordinate inversion in the case of T1 Coordinates, so I presume it will be obvious for the T3 Coordinate system. But the inversion needs to be redone for the case of T3 Coordinates; do you want to take care of this and type up the result? In the (quadratic) case of <math>q^2=2</math>, it may be as simple as replacing <math>\chi_2</math> with <math>1/\lambda_2</math>. --Tohline 11:21, 31 May 2010 (MDT)

Sure. --Jaycall 13:34, 31 May 2010 (MDT)