space curve animations in Maple

One can easily build up complicated animation from relatively simple components, blundering along in a trial and error exploration mode to create each component.

Tutorial and interesting example

This starts with a simple math curve, and then includes bells and whistles to show the hidden geometry of a polar orbit around the Earth which circles the Earth in a plane through the north and south poles that itself is rotating around the symmetry axis of the Earth. This is similar to the geometry of the GP-B satellite gyroscope experiment which tested the influence of the gravitational field of the Earth on the direction of the gyros on board the craft.

Here is the animation exported to a GIF: