This talk will describe the use of Clifford algebra as a natural mathematical framework for engineering mechanics. Modern formulations of mechanics are usually stated in the rather difficult language of differential topology and description of even simple problems requires a multitude of differentiable manifolds. The recent development of Clifford algebra by David Hestenes into a framework called 'geometric algebra' circumvents this, leading to a language which, being far simpler and yet as powerful as the differential topology approach, has obvious attraction for engineering applications.
This is particularly evident in the description of large rotations. I shall endeavour to demonstrate the power of the approach using a few simple problems in rigid body mechanics, before reformulating Simo and Vu Quoc's geometrically-exact finite-element model of the large-rotation, nonlinear dynamics of shear-flexible beams. This re-analysis goes right to the core of structural mechanics, and henceforth, bending moment diagrams will be understood as the graphs of bivector-valued functions.
