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					                                    Re: Goldstein's Classical Mechanics.

Re: Goldstein's Classical Mechanics.


      • From: hetware <massless@xxxxxxxxxxxx>
      • Date: Sun, 27 May 2007 23:58:27 −0400

Eric Gisse wrote:

        On May 27, 3:14 am, hetware <massl...@xxxxxxxxxxxx> wrote:

                Eric Gisse wrote:

                        On May 26, 10:06 pm, hetware <massl...@xxxxxxxxxxxx>

                        A 5 minute reading of Goldstein vs a 5 minute reading of
                        Symon will
                        explain the differences.

                        But keep in mind that Goldstein _starts off_ with the
                        Hamiltonian formalism, wheras Symon doesn't develop it
                        until chapter 9
                        or so.

                I haven't finished it yet, but Chapter 9 /Lagrange's Equations/ in Symon
                so far, very lucid and concise. He also points back to previous chapters
                in his examples showing that, in a sense, this is what we were doing all
                along. I have McCauley's _Classical Mechanics_ which starts out with
                analytical dynamics. I don't know if it is an indication of genuine
                quality, but I noticed that the price I paid for the book a couple years
                back is 20% of the current asking price. I'll probably stick with Symon
                and McCauley for now.

        Oh, you have been using Symon...and like it? huh, how about that.

Re: Goldstein's Classical Mechanics.                                                       1
                                   Re: Goldstein's Classical Mechanics.

See the first post.

        I haven't studied from Goldstein yet, but I have spent some time
        reading it.

I guess I don't make a sharp distinction between reading a book and studying
from it. There are certainly degrees of intensity with which one can
explore the material in a book. I certainly could benefit from working
more exercises. OTOH, I am incapable of reading mathematical physics
without (believing that I am) understanding. My brain just shuts off if I
don't get something. I can't read the subsequent material.

For example, I was reading a book on elasticity, and I hadn't intuitively
grasped what is meant by stress. I could read the words, and follow the
equations, but there was something that hadn't clicked. I figured that it
would come to me if I just kept reading, so I went onto the next section.
For some reason I just couldn't understand the stuff. I tried to go
through the derivations, and it just wasn't clicking. Then I went back an
thought threw the introductory discussion again and finally figured out the
part I had been missing. When I returned to the math I had been stumbling
over, I realized it was trivial algebra and trig.

If I had seen the same equations out of context, they would have been
obvious to me. For some reason, my brain simply refuses to move past
something I don't get. What makes that all the more difficult is that my
standard of understanding is typically far more demanding than that of
others. That's why I hate the presence of the permittivity constant in
E&M. I see this epsilon_o (epsilon sub omicron) in the expression, and I
want to know what it means. It's bullshit! Either explain it before you
use it, or get it out of the #@!$%^ expression!

        Symon is very information−dense − stuff like Louiville's
        theorem [conservation of phase space density] gets a half page at the
        end of a chapter. Goldstein just seems to be something I can read much
        easier, but that may have something to do with the first bits of it
        being fairly easy for me.

If you are talking about variational method, I have to say, I find it to be
potentially misleading. For example, Symon's comment on page 366: "Since
Lagrange's equations have been derived from Newton's equations of motion,
they do not represent a new physical theory, but merely a different but
equivalent way of expressing the same laws of motion." In itself, the
statement is correct. OTOH, there are subtle differences between variation
and differentiation. When used correctly, variation is an operation on a
functional, not on a function.

Re: Goldstein's Classical Mechanics.                                             2
                                    Re: Goldstein's Classical Mechanics.
I've been trying to find the specific example that I recognized years ago
where the generalized momentum and position lead to different results than
would their Newtonian counterparts. It was something like the derivative
of position with respect to acceleration is zero in analytical dynamics,
whereas it is not, in general in Newtonian dynamics. I remember it was a
derivative that a person would not typically perform directly, but it arose
in a derivation.

        Goldstein will be the mechanics book I'll be using in the fall for the
        graduate class in mechanics. Symon was my undergraduate mechanics book
        − went through chapter 12.

I tried that school thing a few times. I always felt like I had a choice
between passing a course or learning something meaningful.

        BTW, how much did you pay for Symon? Before I learned my lesson, I
        paid 150$ for it at a bookstore. It doesn't appear to have gotten
        cheaper over the years, especially considering it was first published
        over a decade before I was born.

$20. Years ago.

Re: Goldstein's Classical Mechanics.                                             3