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Re: DAE system
*To*: mathgroup at smc.vnet.net
*Subject*: [mg104230] Re: DAE system
*From*: Szabolcs Horvát <szhorvat at gmail.com>
*Date*: Sat, 24 Oct 2009 02:40:54 -0400 (EDT)
*References*: <hbou1i$lh6$1@smc.vnet.net>
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. Constraints really mean that the system can be described
by fewer parameters (in this case e.g. just an angle rather than x and
y). 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. In your example F[0] should be m g, i.e. 9.81 (not 10.81) for the
constraint to be satisfied.
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