During my dynamics class, I became particularly bothered by the treatment of frames of reference. We always did our analysis from a "ground frame", which produces counterintuitive behavior. For example, we can imagine two particles moving parallel to each other, both at the same velocity. With the typical approach, each particle has an angular momentum about the other. This didn't sit right with me, as from an inertial frame moving with the particles, we would simply observe two particles with no relative motion to each other, sitting completely still. How could they have an angular momentum relative to each other if they have no relative velocity? 

I set out to derive my own equations, but with the constraint that angular momentum should only depend on the relative velocity of origin and particle. I extended this to rigid bodies and yielded the same equations of motion as the typical formulation (always good!). In short, by choosing a frame which "follows" the origin, we must account for the fictitious forces that arise from being in an accelerated frame. Because the center of mass is not necessarily at the origin, these fictitious forces act with a moment arm from our origin, therefore producing a "fictitious torque" about the origin.