The general motion of the aeroplane

1. Comparatively little progress has been made in the mathematical study of the general motion of the aeroplane. Lanchester’s phugoids, steady motion, and the small deviations obtained when an aeroplane has an actual motion differing slightly from the steady motion appropriate to the conditions of the controls and engines, represent almost the whole of the mathematics of the rigid dynamics of the aeroplane in the present stage of development of the study of the subject. Interesting results have been obtained by L. Hopf and his collaborators (Aerodynamik. by L. Hopf, Springer, Berlin, 1934); but general solutions in explicit form are rarely given. Thus the only information of a general character concerning the dynamics of the aeroplane, i.e. unassociated with steady motion,is the theory of Lanchester’s phugoids; and although Lanchester published this in 1908, reference to the literature on the subject shows that not only has practically no advance been made on Lanchester’s work, but that its significance as a first approximation under certain conditions is not yet fully understood. It is stated by Hopf (ibid.p. 231), but he does not specify the exact conditions, and does not study further developments.