Re: Langrange strange

From: Dirk Van de moortel (dirkvandemoortel_at_ThankS-NO-SperM.hotmail.com)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 11:36:30 GMT

"Bill Hobba" <bhobba@rubbish.net.au> wrote in message news:4CZKd.140819$K7.57550@news-server.bigpond.net.au...
>
> "DavidBowman" <dt041054@yahoo.com> wrote in message
> news:1107056875.826019.103530@z14g2000cwz.googlegroups.com...
> > Mathworld.com has about 5 definitions for "Langrangian", all of which
> > are like trying to find out what division is and being presented with 5
> > algorithms for doing it, when the student really was looking for:
> > "division is the ratio of two numbers".
> >
> > I can tell that the Langragian is basic and general, which makes it
> > interesting. It seems to be some kind of abstract discrete structure
> > like a group or a lattice, and it's used kind of to mean "system".
> >
> > Is it possible to describe the Langrangian such that even a
> > simpleminded fellow like myself can understand?
> >
> > Thanx agin!
>
> Well basically the idea is this. It is assumed we can define a quantity
> called the action for any physical system. Exactly what action is need not
> concern us right now. Now an assumption we make is that the action can be
> written is the form integral something dt or for fields integral something
> dxi dt. What the Principle of least Action (PLA) says is the path the
> particle follows or how the value of the fields change (by which is meant
> the 'path' a particular value of the field traces out - the value being like
> a position coordinate) is the one that makes the action a extremum (usually
> a minimum - hence the word minimum in PLA - but not always). The something
> that it is integrated over is called the lagrangian or lagrangian density
> (depending of if the integral is over dxi dt or just dt). Now the something
> can depend of all sorts of things - field strengths, angles of a rigid
> bodies etc - the exact choice deepens on the problem being considered.
>
> As to why nature should work like this see the following -
> http://aux.planetmath.org/files/papers/234/pathIntegral.pdf.
>
> The following may also be of interest.
> http://www.eftaylor.com/leastaction.html

And this one:
   http://www.courses.fas.harvard.edu/~phys16/Textbook/ch5.pdf

Dirk Vdm

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