Possible Error in Goldstein's Classical Mechanics 3rd Edition

[Laudator]

1st page of Chapter 7, p.276, very last line, p=p'. I get that in Newtonian mechanics, the forces, times and masses are the same in two different inertial reference frames, but shouldn't the momenta measured be different?

 

[Orodruin]

Can you provide more context? Everybody is not sitting with a copy of the 3rd edition at a handy distance.

 

[andresB]

 

[Orodruin]

Velocity is different and so momentum is different. $\vec p’ = \vec p - m\vec v$, where $\vec v$ is the relative velocity between the inertial frames.

 

[andresB]

I think that what the authors wanted to say is that Newton equation remains true if you change the original terms by the transformed ones. Though, doing a literal reading that last equation is wrong.

 

[Filip Larsen]

I have found an (unofficial) errata sheet for the 2nd edition to go with my copy of the textbook, but apart from someone in https://www.researchgate.net/publication/238984277_Errors_in_Goldstein's_Classical_Mechanics pointing out the physical impossibility implied by the front cover figure, I have not been able to find errata for 3rd edition.

From the snapshot above it appears that 3rd edition has significant changes that probably will make it an arduous task to use 2nd edition errata. For what it is worth, it also appears to me that equation (7.2) and its accompanying text, as show in the snapshot above, is new in 3rd edition. The Galilean transformation in equation (7.1) in 3rd edition is equation (7.8) in 2nd edition and it here derived as the "small velocity limit" of the Lorentz transformation.

 

[DrClaude]

There is an erratum available:
http://astro.physics.sc.edu/Goldstein/
Equation (7.2) should read
$$
\mathbf{F}' = \frac{d}{dt'} \mathbf{p}'
$$
as @andresB pointed out above.

 

[Laudator]

@Orodruin, @andresB, @Filip Larsen as well as @DrClaude, thank you all of you for clearing things up! I really appreciate it!

 

[vanhees71]

The newer editions of Goldstein have to be taken with a grain of salt. There are serious conceptual errors in it (concerning non-holonomous constraints, treated wrongly as vasconomic dynamics).

 

[nasu]

What is the meaning of "vasconomic"? Google did not give any hit for vasconomic dynamics.

 

[vanhees71]

Sorry, the right spelling is "vakonomic".

 

[nasu]

Thank you. Google did not suggest it when I was looking for vasconomic. :) It does not know everything. Yet.