Current Progress in the Slender Body Theory 

 exp [(z + z')(m - oJq) Vx - i | y - y ' | K j - im (x - x ' )] (m - c-Jq)^ — 



) ■ f" dm 



^ exp [(z + z')(m- ajQ)2/x + i|y - y' I Kj - im (x- x')] (m-o.^)^:^ 



2i 



where 



j: 



exp [( z + z')(m + Wq)2/x - i|y -y' 1 K2 + im(x - x')] (m + 0;^)^ — 



dm 



r 1 = V(x-x')2 + (y-y')^ + (z - z'y 



r2 = V(x-x')2 + (y-y')2 + (z + z')" 

 X = g/u2 Wq = o/U 



y = ym2 - (mT ^o)Vx2 



tan £ = -(m-Wg)^/xn 



mj "I 



\ = I (x + 2^0 ± 7x2 +4x0;,,) 

 mj 



m^ 1 . . 



I - y (x - 2^0 ± 7x2 - 4x<:^J . 

 m^ J 



On applying the slender body approximation, the asymptotic expression for 

 Green's fvmction along the line y = z = o becomes 



, , ,x 1 1 2i d 



G(x,y, z;x ,y ,z ) =«-^ + 



1 ^ 2 



r , r „ 77 dx 



im(x-x' ) 'I>(m) 



dm 



- 2i 



dx 



f^s 



("1 + ^n)^ 

 ^im(x-x') 2 



m y m ^x 2 - ( m + a.' ) '* 



dm 



(Cont.) 



163 



