Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Action

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?


Joshua Gates

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

Forum for Physics Educators