Lorentz Transformation

( Given x, y, z ,x', y', z',|v|, c, find out Vx, Vy , Vz)

velocity-i +j  + k |v|=  
velocity-i +j  + k |v|=  
velocity V --    km/s velocity of signal km/s
AngleΨ with x-axis (degree) Vx   
AngleΦ with y-axis (degree) Vy   
Angleθ with  z -axis (degree) Vz       
β (V/c) γ = 1/√(1-v2/c2)
x      x'
y                                  y'
z z'
t t'            
origin in S frame (0,0,0,0)    
origin in S' frame , ,
origin in S' frame , ,,
x2+y2+z2 c2t2
R'2=x'2+y'2 +z'2 T'2=c2t'2
 R'2 - T'2    
[t2*v2 -(Vxx+Vyy+Vzz)2/c2]*γ*γ    
(x'-s'(x))2+(y'-s'(y))+(z'-s'(z))2   c2(t'-s'(t))2
A1x   Bx Dx tot
A1y   By Dy tot  
A1z   Bz Dz tot  
   

Remark : From Lorentz1.htm, first determine x',y',z' for a given x,y,z, Vx , , Vy ,Vz and V and c,. when x,y,z and x',y',z' ,V is put here,

                 the result is some what consistent for a set of Vx ,  Vy ,Vz. But for arbitrary values of x,y,z,x',y',z',V,c, there is inconsistency.

                 The same has to be studied further.

On simplification of Lorentz transformation equn, we get

Ax1V2+BxVx + Dx   =0 ; Ay1V2  +ByVy + Dy   =0  ; Az1V2+BzVz + Dz   =0

Ax=(c2t2+x'2) / x'2  ;  Ax1=Ax-1 ;  Bx  = -2c2xt / x'2 ;  Cx = c2( x2- x'2) ; Dx =  Cx  +  V2

Ay =(c2t2+y'2) / y'2 ;  Ay1=Ay-1 ; By  =-2c2yt / y'2;   Cy = c2( y2- y'2) ; Dy = Cy  + V2

Az =(c2t2+z'2) / z'2 ;  Az1=Az -1 ;  Bz  =-2c2zt / z'2;    Cz = c2( z2- z'2) ; Dz =   Cz  + V2

and solve the quadratic equn.