Flight Dynamics with Tensors

Flight dynamics is undergoing a shift from vectors to tensors, taking advantage of the ever increasing computer power to design and analyze complex aerospace systems. The physics are modeled by tensors independently of coordinate systems. Then the tensors are converted to matrices by introducing coordinate systems and evaluated by one of the many matrix computer tools.

This course introduces the novice to tensor flight dynamics, requiring only basic skills in matrix algebra and differential equations. The fundamentals of tensor algebra are introduced by modeling geometrical relationships of expended boosters landing on barges with their related coordinate transformations. As time enters the study, the new rotational time derivative enables kinematics to be formulated independent of coordinate systems in a truly tensorial format, applied to pilots in centrifuges and attitude determination of aircraft. Point-mass trajectories, also called three-degrees-of freedom trajectories, are derived for rockets, hypersonic vehicles, UAVs; while full-up, six-degrees-of-freedom equations lead to the evaluation of the transient responses of missiles and aircraft in state-space format.

The course is supported by the text book “Introduction to Tensor Flight Dynamics”, 3rd Ed published in 2023 by the instructor at Amazon. It provides more details on how to derive the equations of motion from Newton’s and Euler’s laws and features many problems derived from aerospace applications, some of them to be solved with MATLAB®, SCILAB, PYTHON or other matrix processors.

Update Oct 2025: For further studies my textbook : "Modeling and Simulation of Aerospace Vehicle Dynamics” was  just released by AIAA. in its 4th Edition.

Update April 2026: My textbook Introduction to Tensor Flight Dynamics, on which this course is based, can now be downloaded from the Downloadable Section of the Second Lesson: "Manuscript_3rd Ed_2nd Prt_Free".