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From: puchm@cutmcvax.cutmcvax.cs.curtin.edu.au (RichardPuchmayer)
Newsgroups: comp.theory.dynamic-sys
Subject: double pendulum - revisited.
Message-ID: <puchm.672390379@cutmcvax>
Date: 23 Apr 91 07:06:19 GMT
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    Dear netters,
        Having received advice as to which books to look in, I have
        looked in those books.  I now know a bit about Lagrangian
        dynamics:
                L = T - U
                    where :     T = kinetic energy of the system
                                U = potential -- " --
        let d = partial derivative
            D = total derivative
            x = a generalized coordinate
            x. = time derivative of a generalized coordinate

            then:
                dL   D  dL
                -- - --(--) = 0
                dx   Dt dx.

        For ALL the examples I have looked at the derivation of the
        kinetic energy is not too difficult, but the formulation of
        the potential energy seems to be very problem dependent.

        Is there a general method by which to derive the potential
        energy for a system?

        Also:
            For a double pendulum : 
                mass m1 is connected to a pivot by a massless rod of
                length l1, mass m2 is connected to mass m1 (via a
                pivot) by a massless rod of length l2.  The angle
                between the vertical and rod(l1) is th1 and the angle
                between the vertical and rod(l2) is th2.  The only forces
                acting on the masses are gravity and any constraint
                forces through the rods.  Any variable with a dot '.'
                after it denotes the first time derivative of that
                variable.  Two dots '..' denote the second time
                derivative.

                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.

        PS: I've posted this to comp.simulation about a week ago but
        there has been no traffic in that group.  So I'll try this
        one.

        Thanks,
            Richard.

        Thanks,
            Richard.
--
| Some of us are poets, some of us are not. | puchm@cutmcvax.cs.curtin.edu.au |
| Richard Puchmayer, Masters Student at     |         Sorry but I             |
| Curtin University of Western Australia    | don't know any other addresses  |
| I know nothing, so can hold no opinions for myself or others.....:-)        |