InkSprite

Are Lagrangian simulations 100% accurate algebraically?

When programming in a Lagrangian function for determining the position of objects in a system, are previous point values used when calculating new points?

I am still struggling with lagrangian mathematics. I may need to step back to calculous.

Joppy

I think in most practical cases your results are going to be approximate, otherwise we wouldn't bother with numerics. But likely there are contrived examples.

And yes, it is typically the case that after a phase or state space is established (i.e., the system of equations governing the system), the 'future' values, depend on the previous values, along with some scaling factors and so on.

InkSprite

Damn. So I can't reverse a system and get the initial state.

Joppy

Umm. Depends on the system. What are you modelling ?

InkSprite

1000's of particles.
They can pass through each other. They are just points that pull on each other.

Joppy

Is energy conserved in the system (do the particles undergo elastic collisions or exchange heat)?

For nonequilibrium dynamics problems (NEMD), I think running backwards would be troublesome due to stability in your error.

InkSprite

energy is conserved in the system. There is no heat exchanged. No elastic collisions. Is that like two rubber balls bouncing? no, none of that; not brick, or metal or anything. It's all just fields acting on points.

...
At some point int he simulation, energy may be added. From user input.

Joppy

Yes sometimes we have a constant field applied to the system for various reasons.

It's not always useful to think of physical examples when modelling abstract things, they tend to give the wrong impression.
There is no ball that will mimic your reductionist model of interacting particles.


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InkSprite

Okay. I'm not trying to make a ball. I just didn't know what you meant by "elastic" collisions. Like classical physics at the human scale?

I'm just trying to simulate pseudo particles.

What about multiple moving fields?

Joppy

Yes pseudo particles would likely collide elastically in your simulation. This is a fairly unrealistic situation in the real world (except for the refraction of light maybe). But it stands as a good starting point.

The 'fields' i was referring to could be thought of as a gradient which causes items in your simulation to have foccussing/defocussing effects. In that sense, they are 'moving'. However i assume you mean that these gradients could change with time or as specified by some function.