# 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

(10.13a)

(10.13b)

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.

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