Recent content by nylonsmile

Yeah I understand the problem now. Could we just imagine the whole thing is a function of t?

Hmm yeah... But I feel like you could use a difference quotient to find ##\frac{d}{dx}\left( \frac{df}{dx}\frac{dx}{dt}\right) ## but I could be wrong. If I had the functions ##x(t)## and ##f(x)## it seems like I could make a computer work out the required function. Do something like: At ##x##...

Try applying the product rule to: $$\frac{d}{dx}\left( \frac{df}{dx}\frac{dx}{dt}\right) $$

Ok I figured it out. The main problem I had is that I didn't realize that I needed an explicit predictor step. In natural continuation the "predictor" you would normally use is just the value from the previous iteration, but with the new lambda. For Pseudo-arclength continuation (PCA) you need...

I'm struggling to implement a pseudo arclength continuation method for my system. Here is what I have so far. I am trying solve the system of equations F(x, \lambda) = 0 but if I parameterise only by using lambda, I can't get around turning points, so I paramterise by "arclength" s and attempt...

Actually, I'm still not completely on board. When I take the derivative, I use the product rule? And that's where the factor of 2 comes from? I think maybe the dummy indices are what are confusing me. If I think of it as: \mathcal{L} = \frac{1}{2}\left(\eta^{ab}\partial_a\phi\partial_b\phi -...

Wow that makes so much sense! So the upstairs index is just a short-hand that allows you to avoid writing the metric explicitly. Thank you!

Hi, I hope I put this in the right place! I'm having trouble with some of the calculus in moving from the Klein-Gordin Lagrangian density to the equations of motion. The density is: L = \frac{1}{2}\left[ (\partial_μ\phi)(\partial^\mu \phi) - m^2\phi ^2 \right] Now, to apply the...