Recent content by wglmb

oops, haha good point. Thanks.

Well this is it - I don't know what should be considered a function of s. If it's just z-dot then \frac{2R^2}{z^2}\ddot{z} If it's z-dot & z then \frac{2R^2}{z^2}\ddot{z} - \frac{4R^2}{z^3}\dot{z}^2

\frac{2R^2}{z^2}\dot{z}

I have a Lagrangian L = \frac{R^2}{z^2} ( -\dot{t}^2 +\dot{x}^2 +\dot{y}^2 +\dot{z}^2) and I want to find the Euler-Lagrange equations \frac{\partial L}{\partial q} = \frac{d}{ds} \frac{\partial L}{\partial \dot{q}} I'm fine with the LHS and the partial differentiation on the RHS, but when it...

awesome, thanks!

If I have a line element ds^{2} = ... and a curve defined by x^{1} = f( \lambda ), x^{2} = g( \lambda ) etc, and I wand to know if the curve is timelike, spacelike, or null, do I do so by checking the sign of g_{\mu \nu} \frac{dx^{\mu}}{d\lambda} \frac{dx^{\nu}}{d\lambda} ?

Thanks for your help - I think I've got it. As x \rightarrow \infty the signature is 0 As x \rightarrow 0 the signature is 1 So this implies that the metric is not well defined for all 0<\infty, since the signature should be constant.

Ah, I think I see! (I hope) You mean that, since the signature is constant, I can take any x,y,t that I like and calculate it for them?

uh, sorry, I can't see what you're getting at... are you saying I don't need to find the eigenvalues at all?

No, but a later question is "Is the metric well-defined for all 0<x<\infty?" Haven't though about it, but I assume the answer is no, and that suitable restrictions will make it OK. yeeees, but how do I find it? The wikipedia way is to diagonalise the matrix (by finding eigenvalues, then...

Homework Statement I have a metric and I need to find the signature. Homework Equations ds^{2} = -(1-e^{-x^{2}})\ dt^{2} + 6x\ dy^{2} + 9\ dx\ dy + y^{2}\ dx^{2} The Attempt at a Solution In matrix form, the metric is \begin{pmatrix} -(1-e^{-x^{2}}) & 0 & 0 \\ 0 & y^{2} & 9 \\ 0 & 9 & 6x...

Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated! Homework Statement Prove that the function g(x)=1/x is continuous on \latexbb{R}\smallsetminus\{0\}, but cannot be defined at the origin 0 in such a way that the...

It's OK, I've figured it out now. Thanks :)

Ah, I see what you mean - of course! I don't have time just now but I'll work that through later and see how I manage :) Edit: Hmm, well I still get the same matrices A and B, since they come from the double-dotted terms and the x&y terms. The constant terms (now -mg for both of the equations...

Haven't I got that included in the mg(3l+x+y) part of the PE? This comes from mg(l+x)+mg(2l+y) which is mg times the height of the first particle plus mg times the height of the second.