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Modeling Flight Dynamics with Tensors
Highest Rated
Rating: 4.8 out of 5(19 ratings)
321 students

Modeling Flight Dynamics with Tensors

My Master Class
Highest Rated
Created byPeter H Zipfel
Last updated 2/2023
English

What you'll learn

  • Using tensor mechanics instead of vector mechanics to model flight dynamics
  • Deriving equations of motion in three-, five- and six degrees-of-freedom
  • Applying perturbation techniques to flight dynamics
  • Modeling aerodynamics with linear and non-linear derivatives
  • Creating linear equations-of-motion for steady and unsteady flight
  • Learning about gyrodynamics
  • Solving thirty problems relevant to tensor flight dynamics

Course content

4 sections • 12 lectures • 8h 15m total length

  • Introduction25:01

    After my introduction you will appreciate the broad scope of the course, its special terminology, and its foundations based on the Principle of Material Indifference and Einstein's Covariance Principle.  You can also download from Resources the topics of the 30 Problems you will be solving.

  • Tensor Alebra37:54

    Remember your high-school algebra? Now you will extend it to Cartesian tensors (just the bare essentials).

  • Reference Frames and Coordinate Systems49:37

    You will appreciate that frames and coordinate systems are entirely different entities.

Requirements

  • Comprehensive knowledge of traditional flight dynamics
  • Matrix algebra, but no prior knowledge of tensor algeba
  • Some prior familiarity with tensor flight dynamics
  • Access to MATLAB or SCILAB for problem solving

Description

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.

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

Who this course is for:

  • Aeropsace Engineers desiring to deepen their understanding of tensor flight dynamics
  • Students fascinated by the formulation of flight dynamics with tensors
  • Instructrors aspiring to teach modern flight dynamics

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