Inertia Tensor

We all have experienced the effect of mass, foremost as weight brought about by gravitational acceleration, or as inertia when we try to sprint. Yet, how do we sense MOI? If you are an ice dancer, you’ve had plenty of experience. Landing after a double or triple axel, you kick up plenty of ice to stop your turn. Actually, it is your angular momentum (MOI x angular velocity) that you have to catch, and the greater your MOI the greater the angular momentum.

As customary, we divide a body into individual particles and define the MOI of the body by summing over its particles. I shall introduce such familiar terms as axial moments of inertia, products of inertia, and principal moments of inertia. Huygen’s theorem and the parallel axes theorem will show us how to change the reference point or the reference axis. Because we are dealing mostly with vehicles in three dimensions, the moment of inertia ellipsoid, its principal axes, and the radii of gyration will give us a geometrical picture of this elusive MOI tensor. We will conclude this section with some practical rules that take advantage of the symmetries inherent in missiles and aircraft.