Variational Methods

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Original poster: Jared E Dwarshuis <jdwarshui@xxxxxxxxx>

Hi Robert:

Capacitive would be potential energy (T), and inductive would be
kinetic (V). We are not summing the total energy so the minus goes in
the middle betweem T and V.

For the math part you need a good textbook. I regretably do not have a
copy, and I believe that it is out of print. But I particularly liked
a Book written by a guy named French, it was an M.I.T published book.
Waves and Vibration? or Vibration and Sound? Rats I can't remember the
title anymore.

You deserve a good answer in plain talk. Here is what I have gathered
about the Lagrange.......

The Lagrange sort of steps back and says we can examine an entire
system without worying about specific points along the way. When the
lagrange is used to analyze Newtonian mechanics, we can toss out a lot
of vector analysis. WE are no longer interested in one point in
reference to another point or points.

The rough argument (in many instances), is that all the information we
ever really needed was contained in the energy expression. (so why
wory about keeping track of a pile of reference frames )

There are many kinematic problems solved with the lagrange that no one
has ever bothered to recast in the Newtonian mold. (Too much work, or
nearly impossible to get right).

The Lagrange is used to analyze both continuose systems (like rope
resonance) and discrete (or lumped) systems (like mass and spring)

We found that although a resonant transformer is a distributed system.
It has point solutions that are readily compatible with lumped models.
Mechanical solutions were the basic inspiration for our capacitivly
coupled transformers. In some instances we took already worked
solutions and simply changed variables. In any case we used the
Lagrange to see if a particular solution was mathematicaly viable
before building a prototype coil.


There are magnifier designs, just waiting to happen!

Respectfully: Jared Dwarshuis