Physical Geometry by Plane-Based Geometric Algebra

Plane-based geometric algebra (PGA) offers a way to represent Euclidean motions that is directly built on the primitives of affine geometry, and thus provides a seamless framework for objects and their movement. We show how this universal treatment includes the actual physical motions of objects with mass under forces and torques. PGA unifies the linear and angular aspects compactly, and in a coordinate-free manner; inertia maps become simply additive (without displacement terms). We demonstrate the simple equations and straightforward numerical code that result. We show explicitly how to embed the vector-based concepts of the usual classical Newtonian mechanics into the 3D PGA framework, and why it is advantageous to do so.