CURVILINEAR COORDINATES 



101 



5.07 A vector, A, will have three components in the 'directions of the normals 

 to the orthogonal surfaces u, v, w: 



.^rl ^ *^/ ./i ty p~ \. y ( ^LIU 



5.08 



i. div A = hi) 



2. V 



2 _ 



dfAA + _d(AA d /4.\1- 



JMfe/ d^ \^3^i/ 5w \^i^2/ J 

 d i hi d \ d / h% d. \ d f h$ d \ 1 

 9w \/?2/?3 6w/ 6^ \hshi dv/ dw \hihz dw/ J 



curl u A = 

 curl v A = 

 l A = 



6i;V ^3 / 5w\/?2 



_a_ /x\ _ d_ /A\ } 



dw \ hi / du \ hz J } ' 



d (A v \ d (A u \ \ 



^- [i ) - T ( l~ ) r 

 du\}h / dv \ hi J J 



5.09 The gradient of a scalar function, i/>, has three components in the directions 

 of the normals to the three orthogonal surfaces: 



5.20 Spherical Polar Coordinates. 



2. 



= (/). 



x = r sin V cos 

 y = r sin sin 

 2 = r cos 0. 



'o /) 



r sw 



r dS r = r 2 sin d d<, 

 J dSe = r sin 6 dr d <[>, 



d T = r z sin dr d d</>. 



div A 



V 2 = 



r 2 sin 



i 

 /- 2 sin0 



