Novrbin 



K,^ = X^u + Z.w + K.q - X^wu + X-uq - Y^w^ - (Y. - Z-)wq + M-q^ 

 + Y^v + K^ + K^r - (Y. - Z.)vr + Z-vp - M.r^ - K.rp + X^uv 



- (Y. - Z^)vw - (Y. + Z.)wr - Y- wp - X-ur + (Y- + Z-)vq 

 + K^pq- (M. - N.)qr + Y^^v^ 



M.^= X^(u + wq) + Z.(w - uq) + M.q - X^(u^ - w^) - (Z^ - X^,)wu 



+ Y-v + K.p + M.r + Ypvr - Y^vp - K.{p^ - r^) + (K- - N- )rp 



- Y^uv + X^vw - (X^ + Z.){up - wr) + (X. - Z-)(wp + ur) 



- M(.pq + K^qr 



Njj = X.u + Z- w + M.q + X.u^ + Y^wu « (Xp - Y- )uq - Z^wq - K-q^ 

 + Y.v + K.p + N.r - X.v^ - X^vr - (X. - Y- )vp + M-rp + K-p^ 



- (X. - Y.)uv - X^vw + (Xq + Y.)up + Y.ur + Z-wp 



- (X. + Y.)vq - (Kp - M.)pq - K.qr 



I 



(5.5) 



Forces in Horizontal Motions - General 



Especially, for a body which is symmetrical with respect to 

 Its xz-plane and which is moving in the extension of its xy-plane, 

 there are 



Xid = V- Y<,^^- Yr-' 



Ym = YwV + X-ur + Y,r 



»d - -^yv ' ^u 



Njd = N^r + (Y- - Xjuv + Y^ (v + ur) 



+ X^(v - ur) + X^: 



+ X;(u + vr) + X^r' 



+ X;(u^ - v^) + X^(u - vr) 



(5.6) 



By careful application of sound reasoning it is suggested that terms 



830 



