[ODE] solvers, integration (was: more c++, auto-enabling)

[Matthew D. Hancher]

> I think the question on our minds is how their constraint solver
> works; whether it's matrix factoring (O(n^3) a la ODE Step),
> discrete constraints (O(n) a la ODE StepFast), or something
> else.

Actually, the question on my mind was whether they frame the problem
as a linear complementary problem (i.e. an explicit constraint-solving
problem) in the first place.  They seem to claim that they don't.
Featherstone, for instance, looks completely different, though it
seems like that's not what they're doing either.  This question is
largely academic, of course--ODE seems to be making good headway with
the LCP approach--but i'm still curious.

> The integrator doesn't really impact how your solver works, although
> higher-order integrators are always nice for stability. (We use RK4
> for everything at work, btw)

For general-purpose integration of this sort I agree that RK4 is the
way to go.  However we're not just doing integration of a
well-understood function; my hunch is that many of the benefits of
RK4, in terms of being able to increase the stepsize etc., will break
down when you're also trying to keep the collision-detection happy.
Does anyone have any direct experience with that?  I could imagine
that a good RK4 implementation that did collision well could wind up
noticably slower, for people who care about that sort of thing (not
me).  But I certainly haven't tried. :)

mdh