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Re: [Phys-l] Action

Thanks for the replies:

John D - is there an alternative way to calculate K and U (.5mv^2 and mgy) here? Thanks for the point about the total vs. average - I see my issue with that now. I see the usual def'n is dt, but Wikipedia led me to believe (or I led myself) that variables could be substituted to express the dt interval as a dx one - I'm not sure if that's not possible, or if I just did it wrong.

Ken - *headslap* - I had set the initial v as fixed, but there are of course other angles that can work. - The bit about cons. of E was, I thought, a requirement. This is a piece of physics that I'm missing here. Let's say that I don't require cons. of E - I can use any parameterized parabola to get there? That's neat, and I'll have to try different speed parameterizations to check those actions once I have this working.

John M. - another piece of physics that I didn't appreciate; the time requirement. Thanks for the info.

Thanks everyone!

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?


Joshua Gates

Physics Faculty
Tatnall School – Wilmington DE
Johns Hopkins Center for Talented Youth

Forum for Physics Educators

Forum for Physics Educators

Joshua Gates

Physics Faculty
Tatnall School – Wilmington DE
Johns Hopkins Center for Talented Youth