Before I get right into the physics talk, I should briefly describe the game. The idea is to create a multiplayer solar system sandbox. I want simple, vector-style graphics ala Asteroids, and I want a simple economy of trade/piracy, ala Privateer, Freelancer, etc. I have a bunch of ideas of things to add after that, but for now that's the basic idea.
For a first-cut system, I want to model all the ships and asteroids as if they were billiard balls. This is a pretty close approximation for the asteroids, but it's a little rough for the ships. However, at this point it doesn't really matter, as even simple billiards would be better than what I currently have (it's abysmal, I shant share it with you).
I'm using http://billiard-physics.net/ to brush up on my kinematics. I could rederive most of the equations, as I sort of remember most of them, and know how to find them, but I'd rather just save the time and look them up. I have my old college physics text down in the basement, as well as my calculus text. However, I remember these covering mainly static systems, dynamics wasn't really covered that much.
The game won't have a 100% perfect physics system, for example, I plan on setting the maximum velocity to something much slower than speed-of-light. Also, I will have to strike some kind of balance in conservation of momentum, as users arbitrarily accelerating into asteroids in a frictionless environment will increase the total kinetic energy in the system indefinitely (and I'm definitely NOT going to model chemical-to-kinetic energy transformations).
That's it for now. I'm going to Buffalo, NY for the Bills vs. Packers game on Sunday. Most of the code that I have written right now is mostly thumbnail sort of stuff and I will probably throw most of it away.