Hi Folks,

A simple little animation of a bouncing ball. The ball is 100 points on 
a sphere, nearest neighbours connected and triangulated with my convex 
hull macro. To provide ridgidity I also put a mass at the center and 
connected all other points to it.

Comments would be appreciated.

Bye for now,
	Mike Andrews.

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Attachments:
Download 'bball.avi.dat' (470 KB)

Incredible - you're too early - I was going to do this!  ;o)  I'm currently
learning how to code an icosahedron, and I want to use it in mechsim's too..
I want to go a step further, but maybe we can both try this:  Make the ball
jelly-like.

Regards,
Hugo

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Nice, slow, bounce

How does it stop ? Does it bahave like a ball,
or does the movement become "jerky" because
the ball comes to rest on a single traingle ?

WdW


On Thu, 13 Feb 2003 07:56:56 +0000, Michael Andrews
<m.c### [at] rdgacuk> wrote:

>Hi Folks,
>
>A simple little animation of a bouncing ball. The ball is 100 points on 
>a sphere, nearest neighbours connected and triangulated with my convex 
>hull macro. To provide ridgidity I also put a mass at the center and 
>connected all other points to it.
>
>Comments would be appreciated.
>
>Bye for now,
>	Mike Andrews.

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"Michael Andrews" <m.c### [at] rdgacuk> wrote in message
news:3e4b4ef0@news.povray.org...

Very nice. Not sure about the camera following every slight movement (look_at central
mass?)
though.

All the best,

Andy Cocker

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Michael Andrews wrote:
> 
> Hi Folks,
> 
> A simple little animation of a bouncing ball. The ball is 100 points on
> a sphere, nearest neighbours connected and triangulated with my convex
> hull macro. To provide ridgidity I also put a mass at the center and
> connected all other points to it.

Nice.  I already considered adding a macro for such a shape to mechsim.inc
but i did not have the time yet.  It would probably look better if you
only display a sphere with large radius at the position of the center
mass...

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 31 Dec. 2002 _____./\/^>_*_<^\/\.______

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Christoph Hormann wrote:
> It would probably look better if you only display
> a sphere with large radius at the position of the
> center mass...

Provided that the sphere is textured - and rotated to match the movement
of the shape. Because the rotation is half the beauty of this
simulation. :)

Rune
--
3D images and anims, include files, tutorials and more:
rune|vision:  http://runevision.com (updated Oct 19)
POV-Ray Ring: http://webring.povray.co.uk

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Christoph Hormann wrote:
> Nice.  I already considered adding a macro for such a shape to mechsim.inc
> but i did not have the time yet.  It would probably look better if you
> only display a sphere with large radius at the position of the center
> mass...

Hi Christoph,

The first attempts at this had much lower stiffness, so the ball 
distorted considerably when it bounced. This animation was done close to 
the edge of instability with the highest stiffness I could get away with 
for a reasonable time step.

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? 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.

Bye for now,
	Mike.

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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

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 31 Dec. 2002 _____./\/^>_*_<^\/\.______

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Rune wrote:
> Provided that the sphere is textured - and rotated to match the movement
> of the shape. Because the rotation is half the beauty of this
> simulation. :)

Hi Rune,

Yes, this is what I like most as well; the frictive effects of the 
rotation when it bounces. Changing the amount of initial rotation can 
completely change the trajectory of the ball.

I'm going to see if I can uv-map a pigment onto the mesh next.

Bye for now,
	Mike.

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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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