By Jan Roskam
Moment Library replica. San Diego Air and house Museum.
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Additional info for Airplane Flight Dynamics and Automatic Flight Controls
77c) Rl +r = ('PI . 4 are obtained. 57). 4 without loss of generality. 4 all contain products or cross products of perturbed Euler angles or rates; These terms are also referredto as non-linear terms. At this point the so-called smaIl perturbation assumption will be made: the non-linear terms will be assumed to be negligible compared with the linear terms. 4 will also be dropped. 79b) . e. one for which all motion variables are allowed to have non-zero steady state values. It turns out that the majority of airplane dynamic stability problems are concerned with perturbed motions· relative to a wings level,steady state, straight line flight condition with a relatively small flight path angle.
45c): Body axis yaw rate, R IS NOT THE SAME as rate of change of heading angle, $. 47) are acceptable. The reader should keep in mind the fact that in general these approximations are not correct! 19) where it is seen 1}lat the following three components of the gravitational force appear: mg x, mgy and mg z . 48) These components of gravitational acceleration can be written as func;:tions of the Euler angles by recognizing that: kl = k2 . 42) it follows-that: i( - gsin8) "-. 50). 1. 7 REVIEW OF THE EQUATIONS OF MOTION At this point it is useful to review the airplane equations of motion as derived so far.
The earth fixed I\Xis system will be regarded as ail inertial reference frame: one in which Newton's laws of motiollare valid. This means that the rotational velocity of the earth is neglected. Experience indicates this to be acceptable even for supersonic airplanes but not for hypersonic vehicles. 1 (pages 135-137) provides a detailed discussion of this assumption with numerical examples. 1 is assumed to consist of a continuum of mass elements, dm. These mass elements are kept track ol'by the vectors l' which connect the origin ofX'Y'Z' with each mass element.