Article View: comp.theory.dynamic-sys
Article #172Re: double pendulum - revisited.
From: Robert T. Weverka
Date: Wed, 24 Apr 1991 15:41
Date: Wed, 24 Apr 1991 15:41
36 lines
1729 bytes
1729 bytes
mail bounced so this gets posted...
In article <puchm.672390379@cutmcvax> puchm@cutmcvax.cutmcvax.cs.curtin.edu.au (RichardPuchmayer) writes:
>
> T1 = 1/2 * m1 * l1 * th1.
> T2 = 1/2 * m2 * (l1 * th1. + l2 * th2.)
>
> U1 = -m1 * g * l1 * cos(th1)
> U2 = -m2 * g * l2 * cos(th2) * l1 * cos(th1)
>
> Are the potentials correct ?
> If YES, why ?
> If NO, why and what are the correct ones?
> The above questions should indicate a total lack of
> understanding as to the formulation of the potentials.
>
U = m * g * h
so...
you should have
U2 = -m2 * g * ( l2 * cos(th2) + l1 * cos(th1) )
since the quantity in parenthesis is the height.
For the kinetic T= 1/2 m v^2
so ...
v1 = th1. * l
v2 = l * ~th1. + l * ~th2.
where ~ denotes vector quantity. Add these vectorally and compute the magnitude
squared.
Note: check your equations with dimensional analysis.
this would have shown you the error you have in T1 and T2.
have fun. -Ted
Technical Details
Message-ID:
<1991Apr24.154100.17128@colorado.edu>Path:
arc1-ca.pugleaf.net!utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!magnus.acs.ohio-state.edu!csn!boulder!boulder!weverkaReferences:
<puchm.672390379@cutmcvax>Show Full Headers
Complete Article Headers
Newsgroups: comp.theory.dynamic-sys Path: arc1-ca.pugleaf.net!utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!magnus.acs.ohio-state.edu!csn!boulder!boulder!weverka From: weverka@boulder.colorado.edu (Robert T. Weverka) Subject: Re: double pendulum - revisited. Message-ID: <1991Apr24.154100.17128@colorado.edu> Sender: news@colorado.edu (The Daily Planet) Nntp-Posting-Host: espresso.colorado.edu Reply-To: weverka@espresso.Colorado.EDU (Robert T. Weverka) Organization: University of Colorado, Boulder References: <puchm.672390379@cutmcvax> Date: Wed, 24 Apr 1991 15:41:00 GMT Lines: 38