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MathGroup Archive 2005

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Notation for variational calculus?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60712] Notation for variational calculus?
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Sun, 25 Sep 2005 02:36:21 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I came across this very pretty little discussion of the principle of least
action.  I am presenting it here because it demonstrates the use of MathML
in a non-trivial way, and because it provides an example of the
mathematical concepts I would like to represent in Mathematica.

http://physics.ucsd.edu/~epivovar/action1.xml

What I'm wondering is whether there is a useful way of writing (2.1) so that
dl acts as it would on paper. This is the equation:

dl = (dx^2 + dy^2)^1/2 = ((x')^2 + dy)^1/2
where x' = x' (y) = dx/dy

I'm not completely sure what I'm asking, but I believe what I would want is
some way of using the expressions dl, dx and dy so that they are
meaningfully related to l, x and y, and can be used as the DifferentialD in
an integral.

Any ideas on how Mathematica might be used to represent the same
mathematical concepts that are represented in (2.1) above?

-- 
"Philosophy is written in this grand book, The Universe. ... But the book
cannot be understood unless one first learns to comprehend the language...
in which it is written. It is written in the language of mathematics, ...;
without which wanders about in a dark labyrinth."   The Lion of Gaul


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