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*From*: John Mallinckrodt <ajm@csupomona.edu>*Date*: Thu, 7 Jan 2010 11:31:26 -0800

To nail down the path of minimum action you need to fully specify the initial and final "events," i.e., their spatial AND temporal coordinates. As you already know, the path taken by the projectile between any two given starting and ending points will depend on how long you give it to make the trip.

John Mallinckrodt

Cal Poly Pomona

On Jan 7, 2010, at 4:32 AM, Josh Gates wrote:

Hi everyone,

I haven't dealt with action in a long time, so I'm a bit fuzzy on the

particulars at the moment. Here's what I'm trying to do:

Given a starting point (0,0) and an ending point (5m, 9.08m), I'm trying

to show that the parabolic path beginning with a 70 degree initial angle

from +x (the path given by N's laws, kinematics, etc.) minimizes the action.

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?

Thanks,

Josh

--

Joshua Gates

Physics Faculty

Tatnall School – Wilmington DE

Johns Hopkins Center for Talented Youth

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**Follow-Ups**:**Re: [Phys-l] Action***From:*Josh Gates <jgates@tatnall.org>

**References**:**[Phys-l] Action***From:*Josh Gates <jgates@tatnall.org>

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