Awww, I don’t speak c++ at all. I just read it poorly enough to follow Bullet’s source code, vaguely.
Thank you all for clarifying all that!
I’m not particularly attached to Bullet. I picked this one because the Panda manual had many more pages for Bullet than for ODE, and because the built-in character controller seemed nice. Also, the tubes seem enthousiastic.
If I use ODE, how can I create a solid for the player, that always remain vertical, but can push and be pushed by other solids? I’m not asking for a complete source code, but anything that can point me to the right direction is welcome 
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