Circular Motion Model

Previous section: Constant Acceleration Model.

Next sectionGeneral Kinematic Theorem.


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


          Trajectory:  
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.]


          Velocity:  
v = dr / dt = Ωr = ωir          


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


          Path length:  
s = rθ                    Speed:  rω


          Rotor:  
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