**Fourier Analysis of Ocean Tides II** **Feature Column Archive**

## 4. The disk-sphere-cylinder integrator

The center of the disk is fixed. The sphere rolls on the disk. Its point of tangency moves back and forth according to the function `f(t)`, with `0` corresponding to the center of the disk. The cylinder has a fixed axis and is driven rotationally by the sphere. Cylinder and sphere have the same radius. The cylinder does not touch the disk.

Between `t` and `t+dt`, the disk rotates `g'(t) dt` radians. Since the sphere is tangent at radius `f(t)`, points on its instantaneous circle of tangency travel `f(t)g'(t)dt` around an axis parallel to the cylinder, and points on the surface of the cylinder travel the same distance in the opposite direction.