Andrew Coppin wrote:
> Hi folks.
> 
> I still can't quite get this to look how I wanted it to look, but it's still
> very interesting IMHO. Physics is simular to my mesh simulation.
> 
> (I have since improved that mesh, but I when I tried to post, the attachment
> was just *slightly* too big, and I had deleted the source frames by then, so
> I can't rencode... Oh well! Essentially, I used a finer mesh, which looked
> more pleasing. And multiply steps per frame. And a damping method that
> doesn't depend on the framerate...)

The rope does oscillate quite strongly, i think there might be something 
wrong with the damping.

You know with the mechsim patch you can do this stuff fairly easy and 
without the need to do the math yourself. ;-)

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
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Last updated 25 Oct. 2003 _____./\/^>_*_<^\/\.______

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-[I still can't quite get this to look how I wanted it to look]-
How do you want it to look? At the moment it looks to me quite like what it
is a simulation of - that is a lot of masses connected by bungee cords. I'm
not sure quite how to make it look more like a single rope - possibly you
need a force which tries to straighten the links out - this probably ought
to be quite weak but highly damped.

Making the masses on the rope very much smaller might also help. This would
make the system more difficult to simulate though (smaller timesteps
required).

-[So what do ya think, folks?]-
Pretty impressive. Have you simulated any further in time in the simulation
that you've posted. It _looks_ as though it might explode to infinity at
some point - or at least it looks on the verge of being unstable. I may be
being overcritical of your algorithms though - you may have got it exactly
right with very little damping.

One way of checking this (which is used in scientific simulations to make
sure that the errors in the simulation are small) is to find an expression
for the total energy of the system, and to see if that is absolutely
constant, or whether it is increasing or decreasing. Just to insult your
knowledge of physics, you do this by adding up the potential and kinetic
energy, which are given by



m*g*h = the gravitational potential energy for each mass (m=mass,
g=acceleration due to gravity, h=hight above some arbitrary point)


length, where k is such that the force exerted by the spring is k*x and l is
the normal length of the spring. Note that since your springs never exert a
force outwards (if they're the same as your grid springs), this equation
only applies to your springs when x is positive (stretched spring)

If you have some damping, the energy should be decreasing. If you have no
damping, the energy should be absolutely constant. If the energy increases
continuously (even slightly), it means the the simulation is unstable - try
adding damping or shortening the step length.



-Chris

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Chris Johnson wrote:
> [...]
> 

 'normal'
> length, where k is such that the force exerted by the spring is k*x and
 l is
> the normal length of the spring.



where x is the current length and l the unextended length.

in your formula k would be E*A (E=Young's modulus and A=cross section
), 
k by convention is E*A/l.

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 25 Oct. 2003 _____./\/^>_*_<^\/\.______

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Yeah, I know I'm using an unconventional meaning for k. Theres no ASCII
standard 'lambda', which is the conventional one for what I was using. I
prefer putting the spring length into the formula explicitly so that its
clear that the constant in the formula is constant for any spring of that
type.

-[in your formula k would be E*A]-
Yes, assuming that the spring was a bungee-cord or something. Obviously for
a curly spring, the function of force is a somewhat more complicated
function of E and A...

-Chris

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Chris Johnson wrote:
> [...]
> 
> -[in your formula k would be E*A]-
> Yes, assuming that the spring was a bungee-cord or something. Obviously for
> a curly spring, the function of force is a somewhat more complicated
> function of E and A...

Actually it would not be a function of E at all because a helical spring 
works by torsion deformation.

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 25 Oct. 2003 _____./\/^>_*_<^\/\.______

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> -[I still can't quite get this to look how I wanted it to look]-
> How do you want it to look? At the moment it looks to me quite like what
it
> is a simulation of - that is a lot of masses connected by bungee cords.

Yeah, I'm not saying it looks unrealistic (although it seems to be in
slow-motion, which is odd; it isn't supposed to be!) It just doesn't look
how I imagined it looking... lol (I'm sure many POVers know *that* feeling
;-)

> I'm
> not sure quite how to make it look more like a single rope - possibly you
> need a force which tries to straighten the links out - this probably ought
> to be quite weak but highly damped.

I am starting to thing that the only actual problem is that I've got the
parameters set wrong... In particular, I'm not sure the masses match the
sizes of the objects or the forces between them... I'm thinking I'm gonna
try again, using real-world units this time! Say, you don't happen to have
the formula for the volume of a sphere do you? (Oh, and the approximate
density of iron...)

> Making the masses on the rope very much smaller might also help. This
would
> make the system more difficult to simulate though (smaller timesteps
> required).

Mmm... I would have imagines larger masses would be more difficult - more
acceleration and all that... but on the other hand, more subtle movements
would presumably involve lots of small but sudden changes in the forces
acting on the objects...

> -[So what do ya think, folks?]-
> Pretty impressive. Have you simulated any further in time in the
simulation
> that you've posted. It _looks_ as though it might explode to infinity at
> some point - or at least it looks on the verge of being unstable. I may be
> being overcritical of your algorithms though - you may have got it exactly
> right with very little damping.

I think I might definitely run it a bit longer... Just where the simulation
finishes, you can just about see a shock wave propogating up the chain -
just like the real thing! It's really interesting to watch that thing go...

> One way of checking this (which is used in scientific simulations to make
> sure that the errors in the simulation are small) is to find an expression
> for the total energy of the system, and to see if that is absolutely
> constant, or whether it is increasing or decreasing.

Presumably for a damped simulation it should be decreasing. And presumably
in the real world, it's theoritically constant - with "damping" really
involving energy of some kind being imparted to the air, etc. (possibly as
heat, not just motion).

> Just to insult your
> knowledge of physics, you do this by adding up the potential and kinetic
> energy, which are given by
>


OK... I'm not even gonna ask why!

> m*g*h = the gravitational potential energy for each mass (m=mass,
> g=acceleration due to gravity, h=hight above some arbitrary point)
>

'normal'
> length, where k is such that the force exerted by the spring is k*x and l
is
> the normal length of the spring. Note that since your springs never exert
a
> force outwards (if they're the same as your grid springs), this equation
> only applies to your springs when x is positive (stretched spring)

Yes, it's the same spring algorithm. I was originally going to have force in
both directions, but I decided the math was too complicated.

> If you have some damping, the energy should be decreasing. If you have no
> damping, the energy should be absolutely constant. If the energy increases
> continuously (even slightly), it means the the simulation is unstable -
try
> adding damping or shortening the step length.

Makes sense...

Presumably with all these calculations, there's a tendancy for energy to be
lost or gained through rounding errors... but then, the errors are as likely
to loose energy as the gain it, so over all there shouldn't be any big
change...

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> The rope does oscillate quite strongly, i think there might be something
> wrong with the damping.

Possibly... or maybe I just have waaaay too much mass for such feable
springs... who knows? (I have a feeling the masses don't match the radii -
gonna try to redo that part.)

> You know with the mechsim patch you can do this stuff fairly easy and
> without the need to do the math yourself. ;-)

No, I didn't know that.

Thanks.
Andrew.

PS. "..but does 'sense of achievement' mean anything to you? ;-)"

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-[a helical spring works by torsion deformation]-
Yes - isn't this derivable from E given isotropic behaviour of the material?

-Chris

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Chris Johnson wrote:
> -[a helical spring works by torsion deformation]-
> Yes - isn't this derivable from E given isotropic behaviour of the material?

No, you also need the poisson ratio (or formulated more generally: you 
need two independent values to describe the behavior of a linear elastic 
isotropic material).

Christoph

-- 
POV-Ray tutorials, include files, Sim-POV,
HCR-Edit and more: http://www.tu-bs.de/~y0013390/
Last updated 25 Oct. 2003 _____./\/^>_*_<^\/\.______

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-[Any comments?]-
I see what you mean about the ball masses... are you going to post the
source? That might show where the problem lies.

-Chris

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