Previous section: Constant Acceleration Model.
Next section: General Kinematic Theorem.
Motion on a circle of radius r = |r| centered at point c:
Trajectory: x = c + r(t) [Sketch motion map including unit circle.]
(Click here for sketch of motion map.)
Radius vector: r = eiθ(t)r0 [Left multiplying by i, the unit CW bivector, causes CCW rotation.]
Velocity: v = dr / dt = Ωr = ωir
Angle of radius vector: θ Angular speed: ω = dθ / dt (> 0 for CCW motion)
Path length: s = rθ Speed: v = rω
Rotor: R = eiθ Angular velocity: Ω = iω
Rotor equation of motion: dR / dt = ΩR
UCM (Uniform Circular Motion) ⇒ ω = constant ⇒ θ = ωt ⇒ r = eiωtr0
Previous section: Constant Acceleration Model.
Next section: General Kinematic Theorem.