Table 1 Comparison between cycloids on a plane and on a sphere.

From: Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere

 

plane cycloid

spherical cycloid

base line

straight line

adiabatic path n(t)

circle radius

a

rolling speed

equations

curtate/prolate

in/outside

in/outside

arc length

8a

arc area

3Ï€a2

  1. In plane case, the curtate and prolate cycloids are traced by a point at radii b < a and a >b, respectively.
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