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Re: DAE system
*To*: mathgroup at smc.vnet.net
*Subject*: [mg104233] Re: DAE system
*From*: rosenm <rosenm at mail.bg>
*Date*: Sun, 25 Oct 2009 01:02:50 -0400 (EDT)
*References*: <hbou1i$lh6$1@smc.vnet.net> <hbu7ri$7hv$1@smc.vnet.net>
On 24 =D0=9E=D0=BA=D1=82, 09:46, Szabolcs Horv=C3=A1t <szhor... at gmail.com> =
wrote:
> On 2009.10.22. 8:28, rosenm wrote:
>
> > Dear colleagues, can you help me to solve the following system of
> > differential-algebraic equations, wich describes pendulum swinging:
>
> > L = 1; m = 1; Te = 10; g = 9.81;
> > sol = NDSolve[{m*x''[t] == -x[t]*F[t]/L ,
> > m*y''[t] == -y[t]*F[t]/L - m*g, (x[t])^2 + (y[t])^2 - L^2 == 0,
> > x[0] == 0, x'[0] == 1, y[0] == -L, y'[0] == 0, F[0] ==
= 10.81}, {x,
> > y, F}, {t, 0, Te}];
>
> Putting in extra forces is not really a workable way of handling
> constraints. =C2 Constraints really mean that the system can be describ=
ed
> by fewer parameters (in this case e.g. just an angle rather than x and
> y). =C2 See here for a derivation of the diff. eq. for the angle:
>
> http://en.wikipedia.org/wiki/Pendulum_%28derivations%29
>
> (Textbooks on analytical mechanics describe how to handle constraints in
> a general way.)
>
> P.S. =C2 In your example F[0] should be m g, i.e. 9.81 (not 10.81) for =
the
> constraint to be satisfied.
Ok, thank you very much for explanations
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