Why is Mechanics Goldstein difficult to understand?

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The discussion revolves around confusion regarding the equations presented in Herbert Goldstein's textbook on classical mechanics, specifically the internal force between particles. Participants express difficulty in understanding how the equations \(\vec{F_{ij}}=\nabla_{i} V_{ij}\) and \(\vec{F_{ij}}=-\nabla_{j} V_{ij}\) relate to potential energy, which depends on relative distances. There is a mix-up between Herbert Goldstein, the author of the mechanics textbook, and Sheldon Goldstein, known for his work in quantum mechanics. Clarifications are made regarding the correct author and the context of the discussion. Technical issues with posting on the forum are also mentioned, highlighting user experience challenges.
pardesi
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i don't get this what he wrote...
the internal force \vec{F_{ij}} between two particles is \vec{F_{ij}}=\nabla_{i} V_{ij}=\nabla_{ij} V_{ij}=-\nabla_{j} V_{ij}
where the subscript below \nabla_{k}implies the differentitaion with respect to components of \vec{r_{k}}
i can't get how \vec{F_{ij}}=\nabla_{i} V_{ij} or \vec{F_{ij}}=-\nabla_{j} V_{ij}
the potential energy is dependent on the relative distances between the particles hence there is no meaning to the above two equalities
 
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are we talking about Sheldon Goldstein?
 
Oh...

I was thinking about Sheldon Goldstein who deals with quantum mechanics. Sorry
 
nonlocal said:
Oh...

I was thinking about Sheldon Goldstein who deals with quantum mechanics. Sorry
Yes, you are thinking of Shelly Goldstein of Rutgers, the expert on Bohmian mechanics, not Herbert Goldstein, author of the classic textbook on classical mechanics.
 
oops sorry for the inconvinience that was Herbert Goldstein...


P.S:Starnge but i am not able to post with my opera 9.27(because the posting page doesn't load completely) though i am able to do so with FireFox 3 Beta 5...i use Ubuntu 8.04
 
For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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