Lorentz Transformation
( Given x, y, z ,x', y', z',|v|, c, find out Vx, Vy , Vz)
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
Ax1V2x +BxVx + Dx =0 ; Ay1V2 +ByVy + Dy =0 ; Az1V2z +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.