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COORDINATE SYSTEM—FORCES, MOMENTS, AND VELOCITIES
Figure 8.1 illustrates the right-handed set of body axes that will be used in the material to follow. These axes are fixed at the center of gravity relative to the body and, hence, move with the body. The system is easily remembered. x is directed forward, у to the right, and z downward. X, У, and Z are the aerodynamic force components along their respective axes; u, v, and w the velocity components of the center of gravity along these axes; L, M, and N are the moments about these axes; and P, Q, and R are the angular velocities about the x-, y-, and z-axes, respectively. L, M, and N are defined as the rolling, pitching, and yawing moments, respectively. Similarly, P, Q, and R are called the roll, pitch, and yaw rates.
We will see later that for many problems concerning stability and control of an airplane, its motion in the plane of symmetry (x-z plane) can be uncoupled from the motion of the plane of symmetry. The former is referred
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Figure 8.1 Right-handed coordinate system. x, y,z = coordinates; X, Y,Z = aerodynamic forces along axes; u, v,w = velocity components along axes; L, M,N = aerodynamic moments about axes; P, Q,R = angular velocities about axes. |
to as longitudinal motion and treats linear motion along the x – and z-axes, and rotation about the у-axis. Motion of the plane of symmetry, known as lateral or lateral-directional motion, deals with linear motion along the у-axis and angular rotations about the x – and z-axes.
