# FURTHER ASSUMPTIONS

The small-disturbance equations will be slightly restricted by the adoption of two more assumptions, which correspond to current practice. These are

1. The effects of spinning rotors are negligible. This is the case when the air­plane is in gliding flight with power off, when the symmetrical engines have opposite rotation, or when the rotor angular momentum is small.

2. The wind velocity is zero, so that Vе = V

LINEARIZATION

When the small-disturbance notation is introduced into the equations of Sec. 4.7, the additional assumptions noted above are incorporated, and only the first-order terms in disturbance quantities are kept, then the following linear equations are obtained.

 X0 + AX – mg(sin в0 + Ad cos в0) = тАй (a) Y0 + ДТ + mg cos в0 = m(v + u0r) Cb) (4.9,2) Z0 + AZ + mg{cos 60 — Ав sin в0) = m(w — u0q) (c) L0 + AL = lxp – IJ (a) M0 + AM = Iyq (b) (4.9,3) N0 + AN = – I„p + I/ (c) 6 = q (a) ф = p + r tan 0O, p = ф — ф sin в0 Ф) (4.9,4) ф = r sec в0 (c) xE = (m0 + Au) cos 0O – u0A6 sin 60 + w sin 0O (a) yE = и0ф cos в0 + V (b) (4.9,5) ZE = — («0 + Ди) sin в0 — U0A6 cos в0 + w cos в0 (c)