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Re: [Phys-l] Action

On 01/07/2010 05:32 AM, Josh Gates wrote:

Here's how I'm trying to do it (which apparently has one or more flaws):

- I made a spreadsheet, with the columns x, y, v, KE, PE, E, K-U
* x increments in .1 m steps from 0 to 5m
* y is a function of x, defining the path
* v is root(v_i^2-2gy), satisfying cons. of E
* KE and PE are defined in the ordinary way
* E is there to check my formulas, verifying cons. of E
* I average all of the K-U entries to give something similar to the action

Since the x steps are all the same, integrating K-U dx and dividing by
the total delta x should give me the same thing that the average does (I
think). It occurs to me now that there's a problem with paths that go
straight up at any point, but I'm willing to work with that later. My
current issue is that there are other parabolic paths that give a lower
K-U average than the correct path.

Anyone see where I went awry?

The general approach seems reasonable. However, some
opportunities for improvement include:

1) You gave very explicit definitions for all quantities
*except* K and U. It would simplify the discussion if
we had comparably explicit definitions for those, too.

2) Action is the total, not the average.

3) Action is the integral _dt_ so there would never be
any problem with vertical segments.

Also: There is a scintillating discussion of the topic
in Feynman volume I. Well worth re-reading.