Good software for programming animated physical simulations?

AI Thread Summary
For simulating complex physical phenomena such as a double pendulum, particle interactions, or galaxy collisions, various programming environments and languages can be considered. While MATLAB is a familiar choice for some, alternatives may offer greater versatility and efficiency. The discussion highlights the importance of selecting a platform capable of both simulation and animation, with performance scaling based on processor capability and programming skills. Suggestions include exploring professional-grade software like Autodesk 3ds Max, which, despite its high cost, provides advanced features. Additionally, Adobe Flash is mentioned as a more affordable option for students, capable of producing impressive animations. The use of CUDA for leveraging GPU power in simulations is also suggested, indicating a focus on maximizing computational resources for complex modeling tasks.
gomboc
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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:
 
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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
 
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This sounds like a good use for CUDA.
 
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