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American Institute of Aeronautics and Astronautics

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    Course Outline

    Modeling Flight Dynamics with Tensors 



    Course Outline:

    I. Mathematical Modeling in Flight Dynamics
    A. Axioms of classical mechanics

    II. Tensor Algebra
    A. Tensor elements
    B. Tensor products and special tensors

    III. Reference Frames and Coordinate Systems
    A. Heliocentric, inertial, Earth, body frames
    B. Deriving coordinate transformations

    IV. Rotation Tensor
    A. Axis and angle of rotation
    B. Small rotations

    V. Kinematics
    A. Tensor concept of rotational time derivative
    B. Linear velocities an angular velocities


    VI. Translational Equations of Motion
    A. Newton’s second law

    VII. Angular Momentum
    A. Euler’s transformation between referenced frames

    VIII. Attitude Equations of Motion of Motion
    A. Euler’s law

    IX. Gyrodynamics
    A. Poinsot motions

    X. Theory of Perturbations
    A. Equations of motion for steady flight
    B. Equations of motion for unsteady flight

    XI. Aerodynamic Derivatives
    A. Linear and non-linear coefficients

    XII. Linear Equations of Motions
    A. Perturbation equations of aircraft in pull-up
    B. Perturbation equations of agile air-to-air missile