Modeling Flight Dynamics With Tensors

My Master Class

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

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.

Overview

Section 1: Introduction and Fundamentals

Lecture 1 Introduction

Lecture 2 Tensor Alebra

Lecture 3 Reference Frames and Coordinate Systems

Section 2: Newton's Second Law

Lecture 4 Rotation Tensor

Lecture 5 Kinematics

Lecture 6 Translational Equations-of-Motion

Section 3: Euler's Law

Lecture 7 Angular Momentum

Lecture 8 Attitude Equations-of-Motion

Lecture 9 Gyrodynamics

Section 4: Perturbations

Lecture 10 Theory of Perturbations

Lecture 11 Aerodynamic Derivatives

Lecture 12 Linear Equations-of-Motion

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