> The time-step you use will determine the accuracy of the system you are
trying
> to simulate. If it is too long, you will be missing some of the 'detail'
in the
> simulation, this can result in instability in the simulation. On the other
hand,
> if it is too short you will waste processing time unnecessarily.

Yup, sure... the classic accuracy/speed tradeoff found in all computer
graphics algorithms. (Strange, that... *wink*)

> You should also note that some simulations produce stable oscillations in
the
> system which don't ever dissipate. This will be because the system you are
> simulating would in real life oscillate in this way. If increasing the
time-step
> does not remove all oscillation then you can assume they are there to
stay.

Yes... particularly my simulation of elastic springs... you would certainly
expect elastic to oscilate to some degree or other.

> The rate of change of the forces on the particles will determine the
time-step
> you need. If the forces change rapidly then your system will require a
very
> short time-step to correctly simulate the motion of the particle under
those
> conditions. Otherwise a longer time-step will not properly account for
those
> changes in force.

Yes, that's clear.

> For example:
> If you were to apply an oscillatory acceleration of the form:
> acc=A*cos(2*pi*t)
> If you sample the acceleration every 1 second, your simulation will see a
> constant acceleration of magnitude A for the entire duration of the
simulation
> (resulting in particles that start moving and just get faster and faster).
This
> is obviously not the kind of behaviour that an oscillatory acceleration
should
> produce, and is a result of the sample rate being too long.

Mmm... that's just the Nyquist limit comming in to play... sadly, for other
types of simulation, it's not to easy to calculate an adiquate time step
value... I am currently working with 1/250 seconds, and it seems to work
well.

Further to other messages I've posted, I tried a much finer grid (with
smaller masses so the total mass is still unchanged). It seems a lot more
stable...

I was really reacting to what Chris Johnson said - "Euler Integration is the
simplest, least accurate method. [...] Most people here use the 4th-order
Runge-Kutta method". I have no idea what that means! lol

Thanks.
Andrew.

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