Tautochrone
Here is a way to create a cycloid curve:
1. Start with the default scene (just (1) plane).
2. Create a 1.0 radius circle that contacts the plane.
3. Create a 0.125 radius circle at the ball to plane contact point.
4. Uncheck all collision layers for the small circle.
5. Select both circles and glue together.
6. Put angVel = 0.5 in the big circle's postStep event.
7. Set the big circle and plane collision layer to B only.
8. Set Selection>Follow for the small circle.
9. Set brush size to 0.25.
10. Turn off the grid.
11. Position the brush tool directly over the small ball.
12. Hold down the left mouse button.
13. Press the space bar to start the scene.
14. Stop the scene and raise the mouse button when the small circle center is directly under the big circle center.
15. The polygon produced is the path of a rolling 0.25 cylinder whose center of mass traces out a cycloid. This is the solution for the Brachistochrone of a rolling object.
16. Rotate the polygon 180°.
17. Subtract the polygon from a rectangle to create the correct curve.
18. Glue the curve to the background.
