224 SYMPOSIUM ON AERONAUTICS. 



polynomials upon the right hand are of degree 3 or less, the result 

 of the substitution is easy to find. 



For example, when u^^=^J{i — ^"''*)> 



Iu/J = —i — e-'-'i.i28/r), Iuo = — J, 



In- /J = — €-'■*{ .557/r ) , lu-o = O, 



V/ = — c-''(.0285i/r3) =0, Ieo = o, 



/',//= r-''(.0285i/r^)=0, /'eo = 0. 



The equations of motion are 

 «//=:(?-^-^^'(.ooo9 cos 2.42,t -\- .00T,2 sin 2.43^) 



4-^-°''^** (.9991 cos .187^ — .3577 sin .187O — I — (?"'■*(. 1 28/r), 

 zt'//=:£?-^^®'(.io66 cos 2.43^ — -0435 sin 2.43O 



_|_^-.0654f(- — _jQg5 (,Qg .187^ -f .0352 sin .187O — ^"'■H.557A), 

 IOO(9// = £?-•*• ^^*( — .0402 cos 2.43^ — .0278 sin 2.43?) 



_|_^-.oci34f(- 0^02 COS .187^ — .6683 sin .1870. 



The calculation of the constants of integration is much simplified. 

 The terms c^'^/r are retained because the stresses (forces) due to 

 the gust are calculated from du/dt and div/dt to which these terms 

 make an initial contribution — there is an instantaneous initial stress. 

 When t^o, 



du/dt = (.128 — .004 — .008 — .085 — .067)/^ — .016/, 



dzv/dt^= (.557 — .446 — .106+ .007 + .006)/=. 018/. 



These are the initial accelerations and should vanish because the 

 gust though infinitely sharp begins at zero. That they do not 

 vanish is due to an accumulation of errors. 



23. Immediately after the initial instant, however, the first terms, 

 viz., .128 and .557, being multiplied by c''* vanish. The other terms, 

 however, being multiplied by comparatively slow changing func- 

 tions are not altered. Hence immediately after the first instant 

 there are accelerations — .128/ and — -55// along the x and s axes 

 respectively. 



