WOW!!! Thank you! :o
About Runge-Kutta, I have studied it and I have done C-Programming on Runge-Kutta as a coursework, so I think I should be able to understand (if I can recall what I've learnt) what's going on.
But the problem here is that the equations of motion which I am trying to work out (Attachment), includes more than one second order derivatives in a single equation. (Btw, I just realised that the equations I used which I uploaded in the first post has some mistakes.)
How do I go about this?... Do I have no choice but to substitute and rearrange the equations of motion so that there will be only one double derivative term in each?