I've heard of stuff like "three body problems", but what do they mean for physics engines?
Is the situation that if I have two interacting bodies I can input a time parameter to find out where they'll be at any moment, but I have to run a stepped simulation as soon as I add a third body?
If that's the case, anyone mind explaining how the three body problem arises? I'm interested in seeing if there's ways to sacrifice simulation accuracy to treat large systems as a tree of two-body systems.
>>7992777
Trips not enough for an answer?
QUADS
>>7992777
I know it's a scifi book but it does a good job of explaining the three body problem in layman terms. Basically it's impossible to predict the outcome of a three body problem unless you know the starting states of all three bodies.
>>7993348
Why does knowing the starting states matter?
Couldn't any point in time be called the start?
>>7993348
Umm duh?
Law of determinancy says that's true for any system, unless I'm missing something.
>>7992777
The 2 body system can be reduced to the 1 body system and the one body system is solved.
The general 3 body system afaik, is just unsolved because systems of coupled nonlinear equations are hard to solve
>>7993355
That is a terrible explanation.
If I'm not familiar with the exact nature of n-body problems, why would I know all that jargon?
>>7993357
Which part? Have you done a diff eq class yet?
>>7993359
First trimester university student.
>>7993353
>Why does knowing the starting states matter?
It doesn't.
>Couldn't any point in time be called the start?
Yes, but there is no general analytical solution.
Numerically integrate that bitch and hope that the truncation error doesn't run off which it will.
>>7993371
Honestly I'm just looking for an explanation of why you can't use time as a parameter for finding the positions of three bodies when you can do it for two.
>>7993333
WITNESSED
>>7993373
Because the differential equation is too difficult to solve.
>>7993373
You can make a computer program that calculates it, just set up the environment and do the calculation for each flicker of time. The time-complexity goes off the roof compared to an analytic solution, but if you we're going to compute the whole trajectory anyways it's not that bad since you can store the previous calculation in memory.
>>7993383
Im by no means an expert but consider this: how would you approximate the weather in 10 years? It's impossible to get anything even close since it's a chaotic system, which the 3-body system is too, i think.
>>7993383
Too difficult as in hasnt been solved yet.
There is no analytic solution (a function which would give you your bodies position with respect to time) that has given for the general case of 3 bodies.
Someday maybe, some math God will hand us down one, but for now we are stuck at simulating it numerically.
>>7992777
in term of simulation, you use a time "step", depending of the size of this step, the result will greatly change.
>>7993385
Can I see an example of a 2-body equation where time is a parameter?
Also, your answer clears up some stuff, but what problem is it that people keep on running into when they try to make time a parameter? Although looking at a 2-body equation might explain that...
>>7993389
The way you've written that post implies you barely read the OP, given that I use the jargon "stepped" in the second sentence of it but you put your use of "step" in quotes which suggests you think you're introducing new jargon.
Now make like pic related.
>>7993391
>>7993391
>what problem is it that people keep on running into when they try to make time a parameter?
Non-linear equations are hard
I'm sorry for keep going to differential equations, but reality is governed by them.
>Can I see an example of a 2-body equation where time is a parameter?
General solution:
https://en.wikipedia.org/wiki/Orbit_equation
Where theta and r are any functions of time that satisfies these equations...I think.
>>7993401
Oh and the other body is staying still at the origin
>>7993401
I was more curious about an example of a non-periodic two-body problem, such as two charged particles attracting or repelling each other.
Or aren't those possible?
>>7992777
Unlike what other people are saying its generally insoluble because each planet will be labeled by 3 components of momentum and 3 position components, which gives us 18 total unknowns. However you'll only ever find 10 equations, so you end up with a system of 10 equations in 18 unknowns. Its insoluble in its most general form.
>>7993408
An electron and a proton attraction should be the same equation as two bodies falling together
https://en.wikipedia.org/wiki/Free_fall#Inverse-square_law_gravitational_field
>>7993416
Why 10?
>>7993333
damn
>thread dies as it was getting interesting
this ams dildos
>>7993348
>Basically it's impossible to predict the outcome of a three body problem unless you know the starting states of all three bodies.
you can't even solve an ode like [math] \dot{x} = c [/math] without knowing starting states
Work on your reading comprehension
>>7993416
The 18 equations are hamilton equations right?
What are the 10 equations?
>>7993333
Still wondering what >>7993416 meant by "10 equations".
