Michael Andrews wrote:
> 
> [...]
> 
> While I have you on the line (well, sort of :-) could you clarify
> something for me. I originally created the scene with all the object
> sizes ten times bigger. When I reduced the sizes (to give a one meter
> diameter ball) I had to reduce the stiffness as well to get a stable
> system. Is this an expected behaviour, that connection and environmental
> stiffness and damping are size related?

Stiffness and damping are of course size related.  If a connection with a
stiffness of 1000 N/m and a relaxed length of 1 meter is compressed to
half the length it exhibits a larger force on the masses it connects than
if a connection of the same stiffness of only 10 centimeter is compressed
to half the length.  Same applies for the damping.  Apart from that if you
have the masses defined with 'density' you have to remember that their
mass is proportional to the third power of the radius.  

> Are there any rules-of-thumb
> that can help determine what values will give stable systems at
> different scales? Just curious more than anything, a little
> experimentation gets me reasonable deformations.

You can't easily measure the tendency of a complicated system to get
instable in simulation.  Instability is usually caused by 'stiff' systems
but stiffness in this case in not the same as the stiffness of a
connection or an environment.  Damping also has a strong influence on
stability - it can both avoid and support it.

It usually helps not to think in masses, stiffness and damping but in
combined values.  For example for a single mass oscillator (mass and
connection) without damping you can define an eigen angular frequency (i
hope this is the right word, 'Eigenkreisfrequenz' in german):

w = sqrt(k/m)

where k is the stiffness (N/m) and m is the mass (kg).  Large frequencies
usually require small timesteps.  

Another number is the damping ratio:

t = d/(2*sqrt(k*m))

where d is the damping (kg/s) of the connection.  d<1 is considered as low
damping meaning in a single mass system the mass will oscillate.  

Both values do not depend on the size of the system but of course they
only can be given in a single mass system in fact.

Christoph

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