Peter Popov wrote:
> 
> On Fri, 23 Nov 2001 23:24:09 -0500, David Buck <dav### [at] simberoncom>
> wrote:
> 
> >An alternative (but more complicated) is to use a technique called Adaptive
> >Runge Kutta instead of Euler.  Adaptive Runge Kutta is much more stable and is
> >much less likely to give increases in energy during the animation.
> 
> Implicit Euler should do as a start as it won't require much rewriting
> and is almost as fast. That, or central differences. This is a simple
> project, Runge-Kutta (Adams, too) may, IMHO, be overkill.
> 
> Peter Popov ICQ : 15002700
> Personal e-mail : pet### [at] vipbg
> TAG      e-mail : pet### [at] tagpovrayorg

I do believe in doing the simplest thing that could possibly work. 
Although Runge Kutta isn't really all that hard, it may not be needed. 
That last animation is looking much better.  Here's the test:  If you
still use Euler but decrease the step size (step the particle system 10
times for every frame instead of one time for every frame) and the
quality of the result improves, then you know you are having problems
with Euler.  If the result is about the same, the problem is elsewhere. 
If you are having problems with Euler, you should consider other
differential equation solvers like Runge Kutta or Adams (I'm not
familiar with Implicit Euler, so I can't comment on it).  They are
normally needed when the equations get "stiffer".  In this case, it
means that you have stronger forces pushing your particles.  In general,
the stronger the force on the particles, the stiffer the equations
become.  It's ironic, but soft springy systems are easier to simulate
than more rigid ones.

In any case, do the simplest thing possible that makes the system work
for you.  Try increasing the number of steps per frame and see if that
helps.  If not, switching to another differential equation solver won't
help either.

David Buck
Simberon Inc.
www.simberon.com

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