Good software for programming animated physical simulations?

[gomboc]

I'm looking for what might be best for simulating various physical phenomena - some examples off the top of my head might be how to create an animation of a double-pendulum, or a system of 250 particles that are mutually interacting, confined within some box, in an arbitrary external field (like if I wanted to simulate some plasma particle drifts), or trying to use many, many more particles to simulate a collision of two galaxies.

That sort of thing. I'm not sure exactly where to start. My first instinct is to start writing some sort of engine up in MatLab, since it's what I know, but I'm sure there are languages or programming environments better suited to my purposes, and probably more versatile. Basically, I want something that can simulate AND animate the progression of some physical system through time, whose complexity is limited only by processor power and my programming ability.

Any input would be greatly appreciated! A good example of the most complicated sort of thing I'd ever want to try doing with it is here:

 

[Greg Bernhardt]

Something like http://usa.autodesk.com/3ds-max/ will be professional grade, but VERY expensive.

Many very impressive animations can be done with Adobe Flash too. If you are a student it can be very affordable. http://www.academicsuperstore.com/products/Adobe/Flash?uumc=550517&utm_source=search&utm_medium=paidsearch&sissr=1

 

[DavidSnider]

This sounds like a good use for CUDA.