WILSON— AEROPLANE ENCOUNTERING GUSTS. 233 



The complementary functions for v, ^, and r are therefore of the 

 form 



+ Ci.i sin 1.215O, 



+ C, sin i.2i5f), 

 r=C3i^°=""-f C3o^-^-"2' + ^-^2'*'(C33 cos 1.215? 



+ C34 sin 1.215O. 



The particular integrals for any gust may be represented as h, 

 I ^, Ir, and their initial values as h-o, I^q, ho, the derivative of I^ being 

 I' ^ with the corresponding initial values /'^q. 



33. If as before (p. 59) we restrict the possible gusts to those of 

 which the functional form is different from any of the four func- 

 tions entering into the complementary functions, the particular solu- 

 tions must, on substitution, annihilate the right-hand members of 

 the differential equations, and the relations between the constants 

 Cij of integration may be determined from the two equations 



(jD + o.248)z/ + 32.i7<^ — ii5.5r = o, 



0.894Z' -f Oc/) -j- ( 70.6Z) -f 27.0) r = o. 



Hence 



and 

 Further 



and 



Finally 



•2724C11 + 32.17C21 — 1 15-5^31 = 0- 

 .894C11 -\- oQi -f 28.72C31 = o, 



Cii = — 8.326^1, C3i = .259iCi. 



— 8.294C10 + 32.17C00 — ii5.5C3o = o, 

 •894C1. -f oC,o — 575-8^2 =0, 



Ci2=3-797Co2, C32 = .005897C2. 



— .0788C13 + 1.215C1, + 32.17Q3 — ii5-5<^33 == o- 



— i.2i5Ci3 — .0788Ci,-f 32.17^,-115. 5C3, = o, 



