Re: [Phys-l] Action

[Josh Gates <jgates@tatnall.org>]

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!
jg

> 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
> >
> >
> >
> > _______________________________________________
> > Forum for Physics Educators
> > Phys-l@carnot.physics.buffalo.edu
> > https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
> >     
>
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
>
>
>   

--
Joshua Gates

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