REDUCTION OF THE LATERAL-DIRECTIONAL EQUATIONS OF MOTION
The lateral-directional equations of motion are linearized and nondimen – sionalized in a manner similar to that followed for longitudinal motion. The resultant velocity is taken to be nearly constant and equal to U0. V and W are assumed to be small by comparison to U0. The angles ф, в, and ф and their derivatives are also taken to be small. Orders higher than the first for any of these small quantities are neglected. Also, the velocity V is replaced by Uafi. Hence the lateral-directional equations reduce to
у + mgф = mUdP+ R) (10.12 a)
Ь = Іхф-ІхД (10.12b)
N = IZR — Іхгф (10.12c)
The aerodynamic force, У, and moments, L and N, are expressed in coefficient form using S as the reference area and b as the reference length. The coefficients are then expanded in a Taylor series, assuming them to be a function of /3, p, r, Sa, and Sn p and r are dimensionless rates similar to q and
Again a characteristic time t* is defined. However, in the lateral-directional case, the reference length is taken as Ы2.
The dimensionless time r is given by
The mass and moments of inertia are expressed by
Substituting Equations 10.13 to 10.16 into Equation 10.12 results in the final nondimensional, linearized equations of motion governing lateral-directional motion.
In Equation 10.17, all derivatives indicated by a dot are with respect to the dimensionless time r.