The Meaning of the Concept of Potential in Mechanics (and in Physics)

If someone know books/articles dealing with the meaning of the concept of potential in physics (or concerning the physical bases underlying the energy methods of mechanics) then I would very much appreciate getting to know about these.

Please note, when I say physical bases, I mean physical bases—not “simpler/prior mathematical notions/procedures, very easy to work out.” Thus, my query is for material that is primarily conceptual, not mathematical. (As an aside: Mathematical material on this topic is so easy to get that, speaking metaphorically, a stone’s throw would yield a dozen references if not 1200. … But I was talking about treatment that is not exclusively mathematical. Essentially, a counterbalance to La Grange is what I was looking for.)

Also note, by potential, I do not mean the limited context of electromagnetism (EM) alone. Indeed, if you ask me, energy methods are far more valuable in mechanics than in EM primarily because the (statically) indeterminate case is so easy to run into, in mechanics. The momentum approach isn’t, therefore, most convenient.

I have already browsed through Lanczos (The Variational Principles of Mechanics) and find it helpful. Just the right sort of book, even though if I were to have the material to write this book, I wouldn’t present it in the order that he does. … Anyway, apart from this book, is there any other source? That’s the question I have here.

I might as well mention here that for my purpose here, Goldstein (Classical Mechanics) has been a big let down (both in terms of the contents as well as their ordering) and so has been Weinstok (Calculus of Variations). I remember having browsed very rapidly through Morse and Feschback a few years back, but without finding anything directly useful in this context.

So, there. Any indicators/links other than Lanczos would be very much appreciated. If there aren’t any, I guess I might myself write up a research article on this topic.

Thanks in advance for any links/references.

Advertisements