UNSW Pure Maths Seminar: Wildberger -- Rotor coordinates, vector trigonometry and Kepler-Newton orbits

Rotor coordinates provide a new algebraic alternative to polar
coordinates for describing kinematic motion. Here we provide an
introduction to this `vector trigonometry’, relating it to the usual
`tan of half the angle’ substitution in calculus, and using it to derive
some basic facts about motion in fixed and moving reference frames.

These ideas are then used for an alternative approach to one of the key
derivations of modern science: Newton’s explanation of Kepler’s elliptic
orbits for a body moving in a central inverse square law force field.