[ODE] Euler vs. Runge-Kutta and adaptive step sizes

[nlin@nlin.net]

> I have yet to read the first paper you mention, but in the above paper, in
> section 3.2, the constraint
> 
> n . q - alpha >= 0
> 
> is being used

In the first paper I mentioned, this constraint is not present and instead
appears to be replaced by

0 <= n(q^l)^T v^(l+1)   [complementary with]   c_n^(l+1) >= 0

where the superscripts ^(l) and ^(l+1) represent the current and next
configurations. I had thought this was a "velocity-based" formulation;
please correct me if I am wrong. Also in the book Chapter "Time-stepping
methods and the mathematics of rigid body dynamics" (Stewart) equation 1.27
uses this "n . v >= 0" condition. But you are right, "n . v " does not appear
in the second paper mentioned.

-Norman