This reminds me, one of my best friends from uni went from physics into computer animation - not for games but for movies and documentaries. The theory is the same though, to simulate collisions and things like hair fluttering while running requires some complicated mathematics. Once the dynamic system is established then the coder can take some of the heavy trigonometry functions and approximate them with computationally lighter polynomials. I used to help him out sometimes with the maths.

Thanks