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Pyrokenesis
Nov16-03, 04:32 PM
Hello.
I am having trouble answering the following question:
"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."
Am I wrong to assume that r = xi + yj + zk
Any help would be beautiful!
Thanx much
mathman
Nov16-03, 05:37 PM
"Show that the L2 transformation reduces to the L1 transformation when the two reference frames are in standard configuration."
I assume that the source of this question defines what the L2 and L1 transformations are, as well as what two reference frames are being compared. Please elaborate.
Pyrokenesis
Nov17-03, 05:52 AM
The L2 transformations are as follows:
r' = r + γv^[(1 - 1/γ)(r.v^) - βct];
ct' = γ(ct - r.β);
where β = v/c & v^ is the unit vector in the direction of v.
The L1 transformations are:
x' = γ(x - βct);
y' = y;
z' = z;
ct' = γ(ct - βx);
where β = v/c.
All are viewed in the S' frame.
HallsofIvy
Nov17-03, 11:10 AM
We should also require that you define "standard configuration" but I'm going to assume that is with both reference frames moving in the direction of the x-axis [:)].
Yes, you are correct to right r= xi+ yj+ zk. Notice that the difference is that "xi+ yj+ zk" assumes some particular coordinate system ("standard configuration") while "r" does not.
You may also assume ("standard configuration") that v= vi+ 0j+ 0k and that v^= i+ 0j+ 0k.
Pyrokenesis
Nov17-03, 07:27 PM
Sorry. Yes standard configuration is when both reference frames move in the direction of the x-axis.
Thanks I think I can solve it now. [a)]
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