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Near-singular inertia matrix

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--- Quote ---The initial model was derived by hand through the euler-lagrange equation.
--- End quote ---

Wow, that's doing it almost from first principles! See, your problem was that you didn't in turn derive the trigonometry based on the lambda calculus definition of "zero" and "one" :-)

Seriously, though, it sounds like a great way to get an understanding of the basics. I never went that way -- I picked up dynamics from rigid body simulators at a CS level, and had to learn the math "backwards" from the solver down to the constraints down to the actual dynamics/kinematics.

And, what I've learned, is that you really want to keep everything in 3D/4D all the time. Everytime you end up doing trig for anything other than creating a particular instance of an orientation matrix (or quaternion) you end up collapsing the dimensional information, and you have to write it out much more complicated than just using the 3D/4D formulation. And the reason I say 3D/4D is that you probably want to use the 4D matrix representation of translation-plus-rotation, rather than the separate 3D-orientation-plus-3D-offset, because again, it simplifies the math you have to write out.


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