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Problem 1 Consider a paper airplane that has a rubber band driven propeller. The equations of motion for it longitu dinal dynamics can be written as where its state vector is given by the velocity V and the flight path angle y, i.e., xV,E R2, and the control input is given by the thrust u. All of other variables, namely mass m, gravitational acceleration g, lift parameters I, and drag parameter d are fixed constants (a) Let V* > 0 and γ*-0 be the airspeed and the flight path angle for a steady level flight condition, respectively. ie., x. = [V*,0]T İs an equilibrium of this system. Find the expression of V. assuming that u*-0. (b) Linearize the equation of motion about the steady level flight condition defined at (a), and write it as the form of

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