GA2016 – Lecture 3

Applications to 3D dynamics

In this lecture we apply the geometric algebra of three-dimensional space to problems in dynamics. The first step is to replace the concept of an ‘axial vector’ with that of a bivector. Quantities like angular momentum and torque are much more naturally thought of as bivectors – planes in space.

The rotor description of rotations provides a compact dynamical equation for rotations that is simple and robust to code up. As an explicit application we show how easily the framework deals with the problem of a symmetric top.