Exam 1 2026

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AIRPLANE PERFORMANCE AND DYNAMICS A.A. 2025/26 – 1 st EXAM TERM – JANUARY 16 th, 2026 T eacher: C.E.D. Riboldi General Rules •The delivery must beclearly markedwith the SURNAME, NAME and STUDENT PERSONAL CODE at the top of the sheet, inthis orderand all written incapital letters. •Answers must be written using a pen, not a pencil. •Graphs and drawings must be readable and complete. •THE MAXIMUM NUMBER OF PAGES FOR ALL ANSWERS IS FOUR Questions 1. Consider the following generalized expression for the non-linear dynamics and rotational kinematics of an aircraft in flight, where pointGis the center of gravity, andBrepresents a body reference: ( M B G ˙wG B +w G B ×M B G wG B =τ G B ˙eB 321 =S B−1 321 ωB B/I Elaborating on that expression: a. Define explicitly the content ofM B G at matrix level, and that ofw G B at scalar level, for a generic aircraft. b. Define a typical split ofτ G B in terms of aerodynamic/propulsive and gravity forces and mo- ments, highlighting (in implicit form) the most general dependence on state and control vari- ables of these quantities, when assuming a writing in a body reference. Define the content of a typical control array in the process. c. Introduce the hypothesis of static equilibrium, and based on the outcome of pointb.show what is its effect on the equation for dynamic equilibrium in body components. Clearly state and show whether from this writing any state scalar variables can be defined constant. d. Apply the hypothesis of static equilibrium to the kinematic equations in body components, and show whether any components of the rotational rateω I B/I in an inertial frameIcan be defined constant from this writing. (Note: recall where needed thatS B−1 321 R|BT I→B =   cosψ cosθ sinψ cosθ 0 −sinψcosψ0 tanθcosψtanθsinψ1  ). e. Define…