CURVILINEAR COORDINATES 



2. The hyperbolic cylinders: 



*- _ f . x 

 cV c 2 (i - fl 2 ) 



3. The planes: z = w. 



2C is the distance between the foci of the confocal ellipses and hyperbolas: 



4. x = cuv. 



105 



i. 



_ 



dz 2 



9- ^ 



curl u A 



dA 



curl y A = 



dz 



dA z dA 

 dz 



dA z 



'-dz" 





6.31 Parabolic Cylinder Coordinates. 



The three orthogonal surfaces are the two parabolic cylinders: 



y 2 , 



i. 



2. 



And the planes: 



3- 



4- 



5- 



6. 



/ = 



z = w. 



x = c(v u). 



_I U + V _I U + V 



h? = u ' fa 2 ~ v ' 



\/W) 



U + V 



V - 



_d\ d_ (v d 



duv du/^ dv\u dv 



dA, 



