Drag object along cutom pass

Greetings.

Please look at this picture:

I have a guide (curve, part of circle) and an object. I want this object to be draggable along the curve.

The questions are:

  1. Is there any easy way like startDrag() function to solve this?
  2. Any other code? (I guess it should be some Math)

I think some relation could be used here. For example, I drag along x, and I get the right y via some sin or cos relation. Or something like that…