The goal of this project is accuracy. The result of a simulation should be able to match the analytical solution to near machine precision whenever possible. So which physics engine should we use? Can we use an existing one, or do we need to write our own? Are there any existing engines that were built to be accurate?

Are the computations done in those engines directly transferable to "real" units, like m and kg, or were they only written with pixels in mind? What about sub-timestep calculations, so we can calculate the exact moment of a collision between two bodies? How is friction calculated? How are the constraints (for example, pin joints) calculated? Can a body be given an arbitrary moment of inertia (such as solid or shell)?
What kinds of approximations are made to improve performance?

Using an existing engine would greatly accelerate this project's development, and would add credibility--but the main goal is to just have fun, and building a new, hyper-accurate physics engine might open the door to academics and educators.

Need to add docs to functions. Is there a way to automatically generate API docs using comments? Should look into that.