Chapter 4
Chapter 4Dynamical Equations for FlightVehiclesThese notes provide a systematic background of the derivation of the equations of motionfor a flight vehicle , and their linearization. The relationship between dimensional stabilityderivatives and dimensionless aerodynamic coefficients is presented, and the principalcontributions to all important stability derivatives for flight vehicles having left/rightsymmetry are Basic Equations of MotionThe equations of motion for a flight vehicle usually are written in a body-fixed coordinate is convenient to choose the vehicle center of mass as the origin for this system, and the orientationof the (right-handed) system of coordinate axes is chosen byconvention so that, as illustrated inFig. : thex-axis lies in the symmetry plane of the vehicle1and points forward; thez-axis lies in the symmetry plane of the vehicle , is perpendicular to thex-axis, and pointsdown; they-axis is perpendicular to the symmetry plane of the vehicle and points out the right precise orientation of thex-axis depends on the application; the two most common choices are: to choose the orientation of thex-axis so that the product of inertiaIxz=Zmxzdm= 01Almost all flight vehicles
40 CHAPTER 4. DYNAMICAL EQUATIONS FOR FLIGHT VEHICLES x x y 1 f z , zf 1 f ψ ψ y1 x1 y1 θ θ x z z 2 1 2, y2 x z 2 φ φ, x 2 z y y 2 (a) (b) (c) Figure 4.2: The Euler angles Ψ, Θ, and Φ determine the orientation of the body axes of a flight
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