Christoph Hormann wrote:
> 
> 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.  
> 
Ok, I see this. You have to apply more 'work' to compress a one meter 
length by half than you do for a ten centimeter length. Makes sense now :-)
> 
>>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):
> 
Simple harmonic motion perhaps?

> 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
> 
Thanks for this Christoph. It's been a loooong time since I've looked at 
the math for oscillating bodies and this refresher has helped me a lot.

Mike.

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