Why are the choreographies so unstable?

[gabriel.dac]

All of them, with the exception of the one that forms an eight (which was in the previous alpha), don't last too long.  If the problem is the accuracy, then it should be set to a higher number by default (it is currently 50%).

What's up?

[BrandCollision]

I know, this is in fact annoying, but i think its the accuracy and the intigrader is not exactly saved into the choreographies, so try changing the intigrader and the accuracy, it might help

[Gordon Freeman]

I know, this is in fact annoying, but i think its the accuracy and the intigrader is not exactly saved into the choreographies, so try changing the intigrader and the accuracy, it might help

That doesn't make sense. At all.

All of them, with the exception of the one that forms an eight (which was in the previous alpha), don't last too long.  If the problem is the accuracy, then it should be set to a higher number by default (it is currently 50%).

What's up?

Quote from USBlog:

Of course, while these orbits work on paper, they are not always stable when actually simulated. After slight changes in their courses with each orbit, eventually the system falls apart and the bodies either collide or speed off into the emptiness of space.

[BrandCollision]

That doesn't make sense. At all.

How is mine not understandable?! its perfectly understandable!! for me anyway...

Edit by Bla: Edited quotes for relevance.
Bla : y u hax into me comments ):

[Gordon Freeman]

There is no "integrator". You don't save integrators into things, integrators are not nouns.

[gabriel.dac]

If they are supposed to be unstable, then what's the point of having so many choreographies?

[smjjames]

Because it's fun? I dunno.

[im4space]

The choreographies are unstable. It is not the accuracy of the integrator.
They are supposed to be fun, entertaining, and educational.

[Gordon Freeman]

Also it's fun to see stable structures collapse.

[smjjames]

Some of the spirograph type patterns you might find in real life, but it would be the tracing of a single bodys path.

[Estwald]

The point is to show chaos: even a tiny difference in position makes the whole thing break apart later

[Greenleaf]

There is no "integrator". You don't save integrators into things, integrators are not nouns.

It is common practice to use the term "integrator" about a method for doing numerical integration. In US² you can select an integrator and some integrator will be the default integrator. See?


We have a number of different integrators with individual strength and weaknesses. The global default is velocity verlet which is fast and relatively accurate. For choreography we have a different default which is named PEFRL (acronym for performance enhanced Forrest Ruth like, which is an interesting name given that another integrator is called Forrest Ruth).
See https://www.youtube.com/watch?v=IJ2MhXUDZ6o for a basic comparison.


As to accuracy... most of the new systems added are unconditionally unstable which means that ANY error in position and or velocity will break the simulation. A higher accuracy will make the error smaller but it will only delay the chaos slightly.

[Gordon Freeman]

But why is there an error in the first place?

[gabriel.dac]

As to accuracy... most of the new systems added are unconditionally unstable which means that ANY error in position and or velocity will break the simulation. A higher accuracy will make the error smaller but it will only delay the chaos slightly.

So once again, what is the point of having so many choreos? You could at least sort them between stable and unstable. The stable ones should be the firsts in the list. Also, the description of the choreo should change:

-----
Dimensions: 2
# of bodies: 8
Stable?: No
-----

[The Ventifact]

The point, if one at all, is just to see what they all look like. Sure, all the choreography sims become unstable within 5 to 6 seconds, but its not that bad. In fact, I find it quite fun to see it fall apart. What was once uniform and stable, becomes sporadic and unbalanced.

But who knows, maybe GA could figure out how to keep it from falling apart and stay uniform for the whole time the simulation is open. Then, if you wanted to make the choreography unstable, just change the mass or radius of an object and watch it spiral out of control. :)

[Lord DC]

The choreographies might be unstable because GA didn't know they were unstable, thus they might fix it in alpha 13.

[Plutonium]

....most of the new systems added are unconditionally unstable...

They are not broken, so talking about a fix is not relevant. I think GA is well aware of choreos being unstable.

IMHO, it is a good educational tool and it is very interesting to observe HOW things fall apart, at which point, how the mass change affects the system and etc... instead of just looking at bunch of balls drawing a geometric figure infinitely.

[im4space]

The choreographies might be unstable because GA didn't know they were unstable, thus they might fix it in alpha 13.

GA did know that they were unstable. But aren't they still interesting?

[Greenleaf]

They are not broken, so talking about a fix is not relevant. I think GA is well aware of choreos being unstable.

That is correct. It is not an error.
We deal with finite precision math here, which means that if a calculation of, for example, gravity is off by however small a number, it will fall apart. Add more digits to the calculation and it will still fall apart, just more slowly.
In addition to this, in reality, if you (speaking of the unstable setups here) add even a single atom extra mass to one body or move it however small a distance or change the velocity by a tiny amount, it will also fall apart, even with precise math.


Imagine a ball on the top of a perfectly symmetric hill. In theory, if the ball is perfect and it is at the exact top of the hill, it will balance there. In reality, _any_ displacement or asymmetry of the ball or of the hill (while keeping a convex shape, no cheating by putting a dent at the top) will make the ball fall off. The same is true for most of the choreographies.


Main point here is that some physical systems are unconditionally unstable, some are conditionally stable and some are unconditionally stable.


As to why so many... why not?

[Gordon Freeman]

So basically the Accuracy Slider adds more digits to the potentially infinite decimal calculation for gravity?

Everything makes sense

3spookymath