Page 133 - Aeronautical Engineer Data Book
P. 133
Principles of flight dynamics 109
Table 7.1 Motion and perturbation notation
Perturbations
Aircraft axis Ox Oy Oz
Force X Y Z
Moment L M N
Linear velocity U V W
Angular velocity p q r
Attitude
Motions
X Axial ‘drag’ force
Y Side force
Z Normal ‘lift’ force
L Rolling moment
M Pitching moment
N Yawing moment
p Roll rate
q Pitch rate
r Yaw rate
U Axial velocity
V Lateral velocity
W Normal velocity
Where the direction cosine matrix D is given
by: cos cos cos cos – sin
� sin sin cos sin sin sin �
D = – cos sin + cos sin sin cos
cos sin cos cos sin cos
+ sin sin – sin cos cos cos
Angular velocity transformations can be
expressed as:
��
�� � 1 0 –sin �
p
q = 0 cos sin cos
r 0 –sin cos cos
where p, q, r are angular body rates:
Roll rate p = – sin where , ,
Pitch rate q = cos � are attitude
+ sin cos rates with
respect to
Yaw rate r = cos cos datum axes
– sin
