tensors

In this post I want to explore a simple insight about rotating between two orientations. Rotations are notoriously confusing and unintuitive, as evidenced by the fact that Wikipedia lists six different formalisms for representing rotations. Rotations are important to understand, however, because they play an integral role in physics, robotics, biomechanics, 3D animations, and a multitude of other disciplines.

When I first began studying continuum mechanics, tensors were a conundrum to me. I understood how to manipulate them algebraically but obtaining an intuitive understanding of them was a more difficult path. The purpose of this post is to simplify tensors for students who may have also run into the same roadblocks as I did. This post assumes familiarity with orthonormal bases, coordinate systems (frames), and measuring the position and orientation of one frame with respect to another.