If you like videos like this, check out Retrotechtacular on Hackaday. They have a series on mechanical firing computers on navy ship that is nothing short of mech-eng porn, and I mean the classy kind.
That was amazing, thanks. I found the integrator and multiplier especially simple and clever.
I was generally not bad at physics but I remember not getting my head around this one... What a great lesson for decoupling systems. I wonder what's the software equivalent in design pattern land. The facade maybe ?
Not sure about a corresponding design pattern, but the content neatly maps (no pun intended) to function composition.
Is it possible to create a "negative differential gear" that puts more torque into the wheel that is stuck? (in the hopes of forcing it unstuck)
Yes. You are referring to a locking differential, of which there are several types. Some use clutch plates, and will work even if one wheel has no traction at all, others use more complex gearing and can transfer torque from one to another at some multiple (called a Torsen Differential) and cannot drive when one wheel is completely unloaded.