Simple lorentz trans. question

[Ja4Coltrane]

I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

 

[JesseM]

I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

You mean, derive it from the Lorentz transformation? Just take an object with velocity v in one frame, find the coordinates of two events on its worldline (to make it simple the first could be the origin, the second could be the event x=vT, t=T), then find the coordinates of the same two events in another frame moving along the same axis of the first frame's coordinate system, and find (change in position)/(change in time) for the events in the second frame.

 

[bernhard.rothenstein]

velocity transformations

I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

If you intend to derive it without using the Lorentz transformation have a look at
W.N. Mathews Jr. "Relativistic velocity and accelereation transformation from thought experiments," Am.J.Phys. 73 45 (2005)
I will send you a simpler approach to the same problem

 

[bernhard.rothenstein]

velocity transformations

I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

If you intend to derive it without using the Lorentz transformation have a look at
W.N. Mathews Jr. "Relativistic velocity and acceleration transformation from thought experiments," Am.J.Phys. 73 45 (2005)
I will send you a simpler approach to the same problem

 

[pmb_phy]

I have been trying to derive the equation for relative velocity for a while and have had no success. I don't know, perhaps I am slightly misunderstanding SR or something. Does anyone have suggestions for understanding the derivation?

There is a derivation on my website at

http://www.geocities.com/physics_world/sr/velocity_trans.htm

If you have any questions about this derivation then please ask.

Good luck

Pete

 

[robphy]

Using the Lorentz Transformations, one has compose two boost transformations.
The following links will start you off on various methods... but you'll have to finish the calculation.

In matrix form, you multiply two boost matrices, then identify the terms as if it were a single boost [possibly with rotation]. Follow the links, https://www.physicsforums.com/showthread.php?t=121285

Alternatively, one can use vector methods
https://www.physicsforums.com/showthread.php?p=961307#post961307

The k-calculus method is extremely efficient.
https://www.physicsforums.com/showthread.php?t=113915

I'm not a big fan of the usual derivation with infinitesimals.

In the end, for composition in "the same direction", you'll end up with a simple hyperbolic trig identity for tanh.

Which method are you using?