hmv + (Iq + h m) 6 = - G - c_e + Mg . For brevity, write 



I„ = I + h^m 



e o 



Then, inserting the expressions written previously for F and Mq: 



mv + hme + F + (c^ + BS) V - CSe - BS^O = [h6&] 



and 



hmv + I.'e + G + LBSv + (c„ + E^S) 6 - LBS^O = [l+6b] 



O ^ Li 



With these equations may be associated the F and G equations written 

 previously, and also the equations furnished by beam- forcing theory for 

 the response of the beam: 



F = k^ (v - v^) ; G = k2 (e - 6^) [i4Ta,b] 



Vq = a-]_2.F + ai2G '■> ®o ~ ^21^ "•■ ^22^ [i+8a,b] 



Here a , a , a^i ' ^""^ ^pp ^^^ response coefficients to be calculated 

 from the formulas for end forcing if the foil is attached at the end of 

 the beaim, otherwise from the formulas for forcing at an intermediate point, 

 Thus are obtained six fundamental equations in the six variable 



'o^ 

 speed, all of these variables will vary harmonically at the same frequency 



but probably not in the same phase. It is only for such variation that the 



lift formulas are reliable. 



Equations involving only v and 6 as time variables are easily obtained 



by eliminating the other foxir variables. To shorten the notation write: 



k& 



