Modeling Flight Dynamics with Tensors

Join me and take your knowledge of tensor flight dynamics to the next higher level.

After some historical background and definitions, tensor algebra lays the foundation for the tensorial treatment of flight dynamics, together with the two pillars of kinematics, namely the rotational time derivative and Euler’s transformation.

Newton’s Second Law, expressed in an invariant tensor form, independent of coordinate systems, gives rise to three-, five-, and six degrees-of-freedom equations-of-motions.

Euler’s Law provides the attitude equations-of-motion, and insight into the strange behavior of gyrodynamics, as experienced by pilots flying single-engine aircraft.

While the introductory treatment of tensor flight dynamics starts with rigid bodies, here, at the advanced level, I apply the dynamic laws first to particles and then combine them to form rigid bodies.

Of great importance to engineers is my perturbation technique that leads to linearized state equations. This tensorial approach enables the formulation of the perturbation equations-of-motion not only for steady, but also for unsteady reference flight. And the expansion of aerodynamic derivatives to higher orders permits the treatment of nonlinear aerodynamic phenomena.

Practice makes perfect by solving the three problems after each lecture. For verification and for assistance the detailed solutions are included.

The content of this course is based on the graduate lectures I gave at the University of Florida over a span of 15 years.