The equation of motion for autonomous motion in a circle is(1) whereis periodic.

Simple examples includeand

The periodof the motion is the time taken forto increase byand may be found by rearranging (1) to giveand then integrating:

Motion in a circle may have fixed points and terminating motion just like motion in a line.

Example: Find the fixed points for the motion defined byfor

The fixed points are the solutions ofIfthen there are two fixed points atwhereThe fixed point atis stable and the fixed point atis unstable.

Ifthere is a single fixed point atwhich is neither stable or unstable.

Forthere are no fixed points and the motion is purely rotational. The sign ofnever changes sign.