Should I make a physics engine?

I’ve been playing with JBullet lately, and I must say, it’s pretty flippen amazing. But there seems to be annoying little glitches everywhere, that seems to always be literally unfixable, due to how the collision works, ( things constantly shake when a mass’s force is applied to them for instance ). And I was thinking of implementing a physics system into my scene-graph-oriented game engine.

I am planning on this being for “Cross”, my game I’ve been working on for a while, and I’m learning things literally as I go. I’ve never touched scene-graphs, shadow mapping, post-processing, or even 3D lighting until about three weeks ago. Plus, I’m learning allot! So I’ve been thinking of making my own physics engine from the ground up.

All I really need is some basic knowledge on collision and vector-math/physics right? I’ve pretty much got the callback & software architecture side figured out. Does anyone have some good books/articles on how this is usually done?

Thanks in advance.