Transcription of Chapter 4
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Chapter 4
Chapter 4 Dynamical 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= 01 Almost all flight vehicles have bi-lateral (or, left/right)symmetry, and most flight dynamics analyses take advan-tage of this 4.
2. a positive rotation about the y1 axis through the pitch angle Θ to produce the (x2,y2,z2) system; and, finally 3. a positive rotation about the x2 axis through the bank angle Φ to produce the (x,y,z) system. Thus, if we imagine the vehicle oriented initially with its z-axis pointing down and heading North,
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