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

[Martin C. Martin]

Russ, I take it you use Euler integration rather than, say, fourth order
Runge-Kutta?  If so, why?  Would a fourth order Runge-Kutta be a lot
more work?

Also, I'm thinking of implementing my own adaptive step size algorithm,
step doubling as described in Numerical Recipes.  Basically, I take a
step of a large step size, record the positions/velocities of
everything, then "rewinding" everything to before the step and taking
two steps of half the size.  How hard would this rewinding be?  Would I
simply need to record the linear & angular positions & velocities of all
the bodies, and all the forces/torques I've added to those bodies, then
reset them?  Is there much point in doing this with Euler integration?

Thanks,
Martin