a 



GEOMETRY 

 COS 2 /? 



cos 2 7 



2.024 Transformation from a rectangular to an oblique system, x, y, z rec- 

 tangular system: x', y', z f oblique system. 



cos xx = 

 cos yx r = 

 cos zx' = 



cos xy' = k 

 cos yy' mz 

 cos zy' = HZ 



x = hx r + ky' + 

 y = m\x' + mzy r + 

 z = n\x' + n^y' + 



cos y'z' 



COS x 



cos xz = 

 cos 3s' = 

 cos zz 7 = 



2.025 Transformation from one to another oblique system. 



cos xx = LI 

 cos yx' = MI 

 cos zx' = n\ 



A -2 



cos xy' = 

 cos yy' = 

 cos zy = 



A- h 



COS #Z = 



cos yz' = 

 cos 22' = 



k 



+ ky' + 



x = 



z = n\x + n%y 

 m^n^x + (n^h 



+ (fans 



+ 



ll 2 + mi 2 + Wi 2 + 2Wii COS ^Z + 2i/i COS ZX + 2/iWi COS Xy = I, 

 ^2 2 + W2 2 + W2 2 + 2W2W2 COS ^Z + 2^2/2 COS ZX + llwh COS X^ = I, 

 /3 2 + W 3 2 + Ws 2 + 27W3^3 COS JZ + 2Hsk COS ZX + 2/3^3 COS Xy = I. 



ac + y cos :ry + z cos x z = /i#' + ky' + l&', 

 y + x cos xy + z cos zy = m\x' + W2y' + flit*', 

 s + a; cos xz + y cos zy = Wi#' + ^2^' + naz'. 



