The Figures Released

Today, with the data calculated last night (this morning, in fact), the almighty Lord Maverick plotted them out with Matlab. As a showing off, I'll post them here for you.

Well, should Professor Z. Y. Chen ever found this page, and accuse one of his students of "copying these from Pony into his paper", just come and find the author of that paper, and he'll explain.

The trajectory of a particle in a field, with different step h, from 10^-2 to 10^-5.

The energy of the particle mentioned above. It's supposed to be a constant, but error is inevitable in computational physics, the only question is how large the error is.

The motion of a pendulum, solved with Euler's method, a very rough method for ODEs. The line "below" is for the angle it turned in respect of vertical. It should be perfectly periodical, but error make it greatly distorted. The line "above" is for angular velocity, it is even more distorted.

The same pendulum, solved with Velvet's method, a method particularly suitable for 2nd-order ODE with periodical solution. You can see its advantage.