An Interesting Property of Rotational Kinematics

To fly between two locations, a variety of routes are possible. From North America to Europe one could fly directly east or head north over the pole. These flights are equivalent to rotations about axes, one pointing forward and the other out of the North Pole. To see which is which click on one and the other.

Note that the route followed by the red ball is shorter than than that of the blue ball.

The red ball rotates ~90 deg about the red axis

The blue ball rotates ~180 deg about the blue axis.

In the same way, the eye can rotate between two points in a variety of ways.

Some are better than others.

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