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 have bi-lateral (or, left/right)symmetry, and most flight dynamics analyses take advan-tage of this 4.
To write the equation corresponding to Newton’s Second Law, we simply need to set Eq. (4.7) equal to the net external force acting on the vehicle. This force is the sum of the aerodynamic (including propulsive) forces and those due to gravity. In order to express the gravitational force acting on the vehicle in the body axis system, we need
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