Help Deriving Relativistic Momentum Equation 3.9

[albertrichardf]

Hello.
I was reading through this pdf:
https://arxiv.org/pdf/physics/0402024.pdf
on relativistic momentum derivation, and I just can't seem to derive equation 3.9, which is an equation describing the relativistic velocity equation. According to the paper it is supposed to be easy, and apparently follows from equation (3.6). I tried finding the reference but I cannot find it.

Could someone explain how they derive that from 3.6? Thank you.

 

[jedishrfu]

THey mention reference [7], have you tried to find it on the web? It may add to the discussion and help you derive it:

[7] N. D. Mermin, “Relativity without light,” Am. J. Phys. 52, 119–124 (1984). Reissued with a postscript in: N. D. Mermin, Boojums All the Way Through (Cambridge, Cambridge University Press, 1990), pp. 247–265

I think this may lead to it:

http://aapt.scitation.org/doi/abs/10.1119/1.13917

http://aapt.scitation.org/doi/pdf/10.1119/1.13917

 

[albertrichardf]

I did search for the paper before, but it was $30 to access. I found the google preview of the book just now, and it has just the section I need. Thank you.
If anybody else is interested, here it is:

https://books.google.mu/books?id=bf...ge&q=Boojums All the Way Through free&f=false

Not all pages are available but pages 250-252, which contain the equation and its derivation are what is needed for the paper

 

[Battlemage!]

Hello.
I was reading through this pdf:
https://arxiv.org/pdf/physics/0402024.pdf
on relativistic momentum derivation, and I just can't seem to derive equation 3.9, which is an equation describing the relativistic velocity equation. According to the paper it is supposed to be easy, and apparently follows from equation (3.6). I tried finding the reference but I cannot find it.

Could someone explain how they derive that from 3.6? Thank you.

Wow I really like this approach. Great find. Love how easy you can pull out the non-relativistic momentum just by an easy integral. Same with the relatavistic momentum, though it's a bit more work on the integral.

 

[albertrichardf]

Wow I really like this approach. Great find. Love how easy you can pull out the non-relativistic momentum just by an easy integral. Same with the relatavistic momentum, though it's a bit more work on the integral.

I love this approach too. I found the paper a few years ago, but each time I tried reading it I understood only about half of it, so every few months or so I just try reading it through to see if I can follow it. I'm finally able to follow it, and after reading it I love the way it sets up the momentum integral. It is very interesting too because their approach makes few assumptions about the mechanics, so you can easily transfer the ideas over for other mechanics, as they show by deriving both classical and relativistic momentum.