Since the relevant velocity for aerodynamic forces in atmospheric flight is that of the vehicle relative to the local atmosphere, it is essential to he concerned with the motion of the latter. When the atmosphere is, or is assumed to he, at rest relative to the Earth, then FA and *E are the same. If the atmosphere is in uniform motion relative to Fe, with velocity W, then Fa is convected relative to FE with that velocity.

If the motion of the atmosphere is nonuniform in time or space (as is in reality always the case) then FA is so chosen that the space and time averages of the motion of the atmosphere relative to FA taken over the space-time domain of concern in the problem, are zero. The motion of FA relative to Fe is in this case also a constant velocity W. (A treatment of flight in a turbulent atmosphere is given in Chapter 13.)

The velocity of the vehicle mass center relative to FA is denoted by V so that its velocity relative to Fb is

Vе = V + W (4.2,1)


This reference frame has origin fixed to the vehicle, usually at the mass center C, and the Owxw axis is directed along the velocity vector V of the vehicle relative to the atmosphere. The axis Owzw lies in the plane of symmetry of the vehicle if it has one, otherwise is arbitrary. If the atmosphere were at rest, then Ow would trace out the trajectory of the vehicle relative to the Earth, and Owxw would be always tangent to it. The frame Fw has angular velocity b>w relative to Fz. Although by doing so we depart from the general scheme, in the interest of simplicity we shall denote the components ofbiw in Fw by [pw, qw, rw].

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