Date: Mar 3, 2013 10:58 PM
Author: Albert Retey
Subject: Re: Strange behavior of System Modeler
> I have just started studying WSM and the Modelica language by
> implementing the simple pendulum model (class) es. described on p.33 of
> Peter Fritzson's book Introduction to "Modeling and Simulation of
> Technical and Physical Systems with Modelica". The code (pendulum
> equation written as a DAE) is:
> model DAEExample "DAEExample"
> constant Real PI=3.14159265358979;
> parameter Real m=1,g=9.81,l=0.5;
> output Real F;
> output Real x(start=0.5),y(start=0);
> output Real vx,vy;
> m*der(vy)=-y/l*F - m*g;
> x^2 + y^2=l^2;
> end DAEExample;
> I run the example in WSM and I get totally meaningless results. The
> solver is the default one (DASSL) which, I think, is the right one
> for handling DAEs.
> Any ideas?
If your meaningless results look similar to the ones I get it might be a deficiency of the WSM solver. The way it is written the problem is quite "unfriendly" for a numeric DAE solver and needs some more involved tricks to be solved, see e.g.:
where the tricks that Dymola uses to get this solved are described. It came as a pleasant surprise to me that Mathematicas NDSolve (with the IndexReduction option) solves this correctly, so it might be a problem that WRI actually knows how to solve and you probably want to report this.
A workaround is of course to use a formulation that is more "friendly" to the solver, e.g. by reformulating in terms of polar coordinates (but I think Peter Fritzson might well use it in this form to demonstrate something...).
(* Mathematica code for the above: *)