Recent content by TerryW

Hi Tony, You really are a star! Thanks. TerryW

Hi TSny I've now figured out the reasoning behind equations 28 & 29 in Box 25.4 - I just have one issue left which I haven't been able to resolve. It comes from the picture you posted in #6 of the orbit of the particle, which is a line that is normal to the wavefronts it crosses. I thought it...

Sorry, that was a bit sloppy on my part! I feel that there isn't much else to be extracted from this problem - but I have just one question I'm going to look at before I move on. That is: Why does ##\frac {\partial{ \tilde S}}{\partial{ \tilde L}}## produce 'the shape of the orbit' and why is...

Hi TSny I've checked my workings and have found the rogue factor of 4! I had also been doing some work to reconcile the differences between my computed integral and the analytic integral and was having a problem explaining why the analytic integral was greater than the computed integral...

I'm fairly confident about the factor 4 in my expression. The results from using this expression for ##\phi## with the factor 4 are very close to my original computed values. Without the factor 4, the discrepancy would be problematic. I'll see if I can wrangle my expression for ##\phi## into...

Hi TSny I think I've cracked it now. Equation 25.42, for the special values of ##\tilde E= 1##, ##L \dagger = 4##, has the 'analytic' solution: ##\phi = -4 \sqrt 8 ln(tan(\frac{1}{2}arcos(2 \sqrt(\frac{M}{r}))))## I've used my spreadsheet to produce the orbits for the computed integral and...

I've abandoned the attempt to get a path using the 'interference' method. There is a problem creating curves for values of ##\tilde E < 0## because the particle ends up at distances r/M >4, they don't have the energy to scale the full height of the potential, so the interesting part of the curve...

Thanks for doing this. I'll carry on with my attempt to get the path by the 'interference' method.

Hi TNsy I'm still working on this, albeit slowly. (It's Spring so I need to get my vegetable seedlings going for one thing) I have worked through (27) and derived the same answer as you (don't know why the square root signs have disappeared in the quote) but that immediately gave me a problem...

I've had my think and run my model for a value of r/2M = 163 and found that my curve spirals 5+ times before it reaches r/2M = 4. I've attached a screenshot of my initial data. I assume that the result of the integral is an angle given in radians. I think that the spiralling arises because even...

Our different plots are not exactly alike - I'll have a think and get back to you. I'll see if I can do something to replicate your generation of the trajectory. I really like what you have done! Terry

My spreadsheet is now working well and I have plotted the orbit of a particle starting the integral at r/M = 193. I figured out a way to get Excel to produce a radial plot using some macros - I just haven't been able to get rid of the line joining the beginning of one of the orbit segments and...

Hi TSny Lovely to hear from you again. Hope you are keeping well. I've used my spreadsheet to do the integration and then I hit on the idea of plotting my results on a radar chart where the result of the integration is the angle and the path is rendered by the value of r/2M plotted on the...

I am attempting to construct the locus in the r,θ diagram of points of constant dynamic phase S~(t,θ) for t=0 and for values ofL~=4M,E~=1 I begin with Equation (27) in Box 25.4 which is: ##\tilde S = - \tilde E t +\tilde L \theta ## ##+ \int^r [\tilde E^2 - (1-\frac{2M}{r})(1+\frac{\tilde...

I actually feel that you’ve helped me a great deal with this problem and the exchange has improved my understanding of what parameterisation is all about and that ##\frac{d}{d\lambda}## is something more abstract than classical momentum. So you’ve most certainly helped me more than you think you...