I am a newcomer to working with differential algebraic equations and I am trying to work my way through Matlab's pendulum DAE system example:
https://www.mathworks.com/help/symbolic/solve-differential-algebraic-equations.html. $$\left\{\begin{aligned} m\ddot x(t)&=T(t)\frac{x(t)}{r}\\ m\ddot y(t)&=T(t)\frac{y(t)}{r}-mg\\ r^2&=x(t)^2+y(t)^2 \end{aligned}\right.$$
I understand what's going on here at the high level, but I find when I tweak the code in "Step 6" to ask for a simulation that lasts longer than the $0.5$ seconds of the code example, it refuses to solve past $x=0.5$. For the second run of the code in Step 6 (with the changed parameter value), it similarly stops at about $x=0.7$. It appears to be the $x$ value reaching 0 that breaks the example. Is there an obvious reason why that would happen?
I get no error messages except for the warning shown in the link above, which I've copied here:
Warning: Failure at t=5.067150e-01. Unable to meet integration tolerances
without reducing the step size below the smallest value allowed (1.800123e-15)
at time t.
I'm hoping to use the same process to solve more complicated sets of DAEs, but this doesn't inspire much confidence. Am I heading down the wrong path?
Thanks for any insight.