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Side velocity and downward velocity reSllectiyely. 18h) for the distance components which locate masS elements in the air,plane. o iChapter 1 9 Equations of Motion and Axis Systems y Z Z' (Earth-fixed) Aerodynamic and Thrust Forces Acceleration of Gravity Z Aerodynamic and Thrust Moments Z Linear and Angular (Rotational) Velloci'tits Fipre 1,2 Definitions of vector Components in the AiQllane Equations of Motion In Chapter 6 it will be shown that many of these inertial properties have a very significant influence on the response behavior of the airplane in flight as weIl as on the flying qualities of the airplane.

F T, mgsin~cose + FA,. 51b) Force along Z: m(V .... 51c) 2. For the moment eqyations in the airplane bruly fixed axis system XYZ: + (Izz - lyy)RQ = LA + ~ Rolling moment about X: I""P - IxzR - IxzPQ Pitching moment about Y: + (I"" - Izz)PR + Ixz(P2 - R2) IzzR - IxzP + (Iyy - Ixx)PQ + I",QR Yawing moment about Z: Iyy(! 52c) 3. 52) are referred to as the general airplane equations of motion. That is a rather generous description since many assumptions have been made in their derivation. Many of these assumptions serve to reduce the ' generality' of these equations!

That is a rather generous description since many assumptions have been made in their derivation. Many of these assumptions serve to reduce the ' generality' of these equations! the motion variables. That will be dode in Chapter 3. 53) form a set of nine differential equations in nine variables: the velocity components U, V and W, the angular rate com- Chapter 1 21 Equations of Motion and Axis Systems ponents P, Q and R and the Euler angles qt, 9 and Ill. By a process of elimination of variables it is also possible to think of these equations as a set of six differential equations of motion in six variables: either U, V, W, P, Q and R or U, V, W, qt, 9 and Ill.

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