CHAPTER 6 CURVILINEAR COORDINATES  2U   ,  Q6. Given the coordinate transformation U1 xy, x y U z 2 2 2 3 (a) Show that the coordinate system is not orthogonal x, y, z ,U ,U U1 2 3 (c) Find dS2 (c) 1 2 Ans. (b) (x )(dU12  ) 4xydU1dU y dU 2 2 22 2  ds 2 (x )2 y  dU 2 2 32  (dU12 )  U dU 2 22 2 2(U )  U12 22 97  dU 32
CHAPTER 6 CURVILINEAR COORDINATES Q6. Given the coordinate transformation U1  xy, 2U 2  x 2  y 2 , U 3  z (a) Show that the coordinate system is not orthogonal x, y, z U1 ,U 2 ,U 3 (c) Find dS2 Ans. (b) 2 1 (c) ds 2  (x 2 y 2 )(dU12  dU 22 ) 4xydU1dU 2 (x 2 y 2 )2  dU 32  U 2 (dU12  dU 22 ) 2 2(U 22  U12 )  dU 32 97