Davenport chained rotations

Okay, let's play a game where you have a toy with several shapes like a square, a triangle, and a circle. You want to rotate them in a special way so that they make a pattern like a chain that loops around.

Davenport chained rotations are a way of doing this with numbers instead of shapes. Instead of rotating shapes, we rotate numbers around a circle. But not just any numbers, special numbers with certain properties.

The numbers we use are called "quaternions", which are like numbers with four parts instead of two that you might be familiar with. Rotating quaternions is a bit tricky, so we use a special technique called "SLERP" to make them spin in a smooth way.

To create the chain pattern, we take several quaternions and rotate them in succession, like a chain of rotations. Each quaternion is chosen to be a certain distance away from the previous one to make the chain bend in just the right way.

Imagine taking your toy shapes and spinning them one by one in a certain order to make a cool chain pattern. That's similar to what we're doing with Davenport chained rotations, except instead of toy shapes, we're using special numbers called quaternions.