NOTATION FOR SMALL DISTURBANCES
The reference values of all the variables are denoted by a subscript zero, and the small perturbations by prefix Д. When the reference value is zero, the Д is omitted. All the disturbance quantities and their derivatives are assumed to be small, so that their squares and products are negligible compared to first-order quantities.
The reference flight condition is assumed for convenience to be symmetric and with no angular velocity. Thus v0 = p0 = q0 = r0 = ф0 = 0. Furthermore, stability axes are selected as standard in this book, and thus w0 = 0 for all the problems considered. u0 is then equal to the reference flight speed, and в0 to the reference angle of climb (not assumed to be small). In dealing with the trigonometric functions in the equations the following relations are used:
sin (0O + Ав) = sin в0 cos Ав + cos в0 sin Ав = sin в0 + A0cos 60
cos (в0 + Ав) = cos 60 cos Ав – sin в0 sin Ав (4.9,1)
= cos в0 — Ав sin 6>0