-Ar 



where 



Thus 



dS = /EG-F drd6 = H drd0 (4) 



v - ~ 2 2 



E = x„ • x„ = r sec 



G = x • x = (9X +Z, ) 2 + 1 (5) 



r r r r 



F = x • x Q = X(0X +£ ) 

 r r r 



1/2 

 dS = [X 2 +r 2 +r 2 (0X +C ) 2 ] drd6 (6) 



The unit vector normal to the reference surface is 



x„ x x x n x x (-ri+r(X Q+T, )j+Xk 

 r 9 r r r 



v* r i /£? 



(7) 



If X and Z, are independent of r, the normal vector in Equation (7) is on the cyl- 

 inder, r = constant. That is, the radial component of the normal vector is zero. 

 Two convenient unit vectors tangential to the reference surface are 



x fi x fl x fl 



= g- (8) 



/E n l 



and 



