Recent content by radiogaga35

Schwarzschild metric - rescaled coordinates Hi, I've been working through a problem (no. 14 in ch. 9) of Alan Lightman's book of GR problems. I can't understand one of the results that are stated without proof. Basically it amounts to a rescaling of coordinates. I know that to first order...

Thank you!

Hi...would appreciate any suggestions re the following integral which has appeared in a celestial-mechanics calculation: I = \int_0^{2\pi } {\frac{1}{{(1 + e\cos \theta )^3}}d\theta } where 0 < e < 1. Integration by parts seems a sensible approach but for some reason I can't get sensible...

Ok, I applied the aforementioned approach (with appropriately-adapted Newton-method implementation) to a trial problem and it worked perfectly. In principle it seems like a sensible enough approach, but I'm not very clued up on BVP methods, so I'm not sure if there is any theoretical reason...

Given the boundary value problem (primes denote differentiation w.r.t x): \begin{array}{l} y'' = f(x,y,y') \\ y(a) = \alpha \\ y(b) = \beta \\ \end{array} the nonlinear shooting method may be implemented to solve the problem. A bisection algorithm may be used or, with a little...

Ok, thanks for the suggestion, I'll take a look!

Hi there Griffiths uses a nice notation for the vector from the source point to the field point --a "squiggly r" -- in his E-M textbook. He calls it a "script letter". It makes many ugly expressions look much simpler. Anyway, nice as it is, does anyone who has used Griffiths know how to...

Ok, found one or two articles, but now a different difficulty: Any suggestions as to how I can estimate the spring constant ('k') in this atomic oscillator model? The (imaginary) spring being the electrostatic force bonding the electron to the positive nucleus. Thanks

Hi there I found the following nice webpage that gives a brief discussion of the Lorentz Oscillator Model of the atom: http://webphysics.davidson.edu/Projects/AnAntonelli/node5.html. It's part of someone's honours thesis. (Unfortunately the pictures are very small, but nevermind.) Can...

Aha, thank you for your suggestions, I like the "Ella Fitzgerald" and piezoelectric crystal example. The former seems particularly fun, and a striking example of resonance...although I suppose it would be easier to study the effects of damping/different natural angular frequencies/etc. in the...

Hi there I need some advice, please: can you suggest any interesting cases of a driven, damped harmonic oscillator? I need to write a report (part of some assignment) on the mathematical model/behaviour/etc. of some real-world driven oscillator. No problems with the math, I'm just looking...

Ok, nevermind, got it figured out! Just used a bit of geometry

Hi there I am trying to sum many cosines of different amplitude and phase shift, but same ang. frequency (it's not a coursework question). My first thoughts are to sum them two at a time (to simplify matters?), probably using complex numbers. I tried doing it symbolically in MATLAB but it...

Ok, I see where I went wrong. Thank you for your help! HallsOfIvy, the polar co-ordinate transformation seems like a very good approach. Thanks a lot!

Hello I've only recently begun studying (in math, anyway) functions of two variables, so forgive me if my terminology is vague or incorrect (or if I am completely misguided!). Suppose I want to find the limit of f(x,y) as (x,y) --> (0,0). Now, I know that the limit will exist (other...