Radial velocity and angular momentum, with geometric algebra
Peeter's math and physics play
In this video, we compute velocity in a radial representation. We use a scalar radial coordinate, and leave all the angular dependence implicitly encoded in a radial unit vector, r-hat. We find the geometric algebra structure of the r-hat derivative in two different ways, then derive the conventional triple vector cross product equivalent for reference.
We then compute kinetic energy in this representation, and show how a bivector-valued angular momentum, falls naturally from that computation.
Prerequisites: calculus (derivatives and chain rule), and geometric algebra basics (vector multiplication, commutation relationships for vectors and bivectors in a plane, wedge and cross product equivalencies, ...)
Errata: A small error: @4:12 and after that -- I've written bold r, instead of bold x. That mistake is propagated into the expression for L, occurring a few more times.
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or my book (Geometric Algebra for Electrical Engineers), which is available for free in pdf form at:
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