Circular Motion Model

Previous section: Constant Acceleration Model.

Next sectionGeneral Kinematic Theorem.

Motion on a circle of radius  r = |r|  centered at point c:

r(t)              [Sketch motion map including unit circle.]

                                                            (Click here for sketch of motion map.)

          Radius vector:  
eiθ(t)r0          [Left multiplying by i, the unit CW bivector, causes CCW rotation.]

v = dr / dt = Ωr = ωir          

          Angle of radius vector:  
θ          Angular speed:  ωdθ / dt    (0 for CCW motion)

          Path length:  
s = rθ                    Speed:  rω

R = eiθ                            Angular velocity:  Ωiω

          Rotor equation of motion:  dR / dt = ΩR

UCM (Uniform Circular Motion)        ω = constant        θ = ωt        eiωtr0

Previous sectionConstant Acceleration Model.

Next section: General Kinematic Theorem.

© David Hestenes 2005, 2014