My Math Forum The N-Body problem, what can we know?

 Physics Physics Forum

 May 15th, 2017, 07:01 AM #1 Member   Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations The N-Body problem, what can we know? Is there a way to setup an n-body system and know what state it should be via "common sense" or a simple proof that works because the system is non-chaotic? Let's say you have 3 bodies at the points of a equilateral triangle. They all pull on each other with the same force. Since the net force is basically a virtual particle that's the center of the other two, and all virtual particles are equilateral, the system should be predictable, non-chaotic. It's essentially 3 independent 2-body problems. Are there other states we can prove at any given T? The above problem I think can be solved with integrals.
 May 15th, 2017, 05:03 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,600 Thanks: 546 Math Focus: Yet to find out. No. Chaos will emerge. I one of your other posts, Mashcke highlighted the idea of differential equations applied to a 'predator-prey' system. This is a good starting point. In fact the Lotka-Volterra model helps us to understand chaos better due to its simplicity, maybe go have a look at those, then come back to the three body problem. I mention this because in both cases we are dealing with a system of coupled differential equations. The three body problem involves 3 coupled second order differential equations. It has been shown on several accounts that chaos will be exhibited in these systems, and often is often said that dimensionality >2 is required.
May 16th, 2017, 06:58 AM   #3
Member

Joined: Dec 2016
From: United States

Posts: 53
Thanks: 3

Math Focus: Abstract Simulations
Quote:
 Originally Posted by Joppy No. Chaos will emerge. I one of your other posts, Mashcke highlighted the idea of differential equations applied to a 'predator-prey' system. This is a good starting point. In fact the Lotka-Volterra model helps us to understand chaos better due to its simplicity, maybe go have a look at those, then come back to the three body problem. I mention this because in both cases we are dealing with a system of coupled differential equations. The three body problem involves 3 coupled second order differential equations. It has been shown on several accounts that chaos will be exhibited in these systems, and often is often said that dimensionality >2 is required.
Well, the idea is, if I can know an equilateral system with T, then I could create a program that brute forces the topology of logic that can come to those results. Then try it with a more complex system.

May 16th, 2017, 08:03 PM   #4
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,600
Thanks: 546

Math Focus: Yet to find out.
Quote:
 Originally Posted by InkSprite brute forces the topology of logic
?

 May 21st, 2017, 04:54 AM #5 Member   Joined: Dec 2016 From: United States Posts: 53 Thanks: 3 Math Focus: Abstract Simulations Instead of talking. I'm going to focus on producing. There are a lot of programs I need to write. I'm going to try to break down all aspects of an N-Body system. Another repeating state is if you spin the equilateral points while they attract each other. if it rotates 60 degrees and the speeds are just right, you could possibly have a system that looks identical to its initial state. Brute force pattern finding
 May 21st, 2017, 09:33 AM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,327 Thanks: 2451 Math Focus: Mainly analysis and algebra Your program runs in discrete time, not continuous time. It's therefore an approximation. Because the system exhibits chaotic behaviour, the small deviations from reality that your model contains will throw the results off in unpredictable ways. That's not to say that we can't predict what happens in certain trivial cases (when symmetry can be used to simplify the problem), but there's not a lot of interest in trivial cases (by definition). Last edited by v8archie; May 21st, 2017 at 09:35 AM.
May 21st, 2017, 01:48 PM   #7
Member

Joined: Dec 2016
From: United States

Posts: 53
Thanks: 3

Math Focus: Abstract Simulations
Quote:
 Originally Posted by v8archie Your program runs in discrete time, not continuous time. It's therefore an approximation. Because the system exhibits chaotic behaviour, the small deviations from reality that your model contains will throw the results off in unpredictable ways. That's not to say that we can't predict what happens in certain trivial cases (when symmetry can be used to simplify the problem), but there's not a lot of interest in trivial cases (by definition).
It is continuous if you can simplify each attraction down to a 2 body system. Rotation doesn't change anything.

May 21st, 2017, 03:22 PM   #8
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,600
Thanks: 546

Math Focus: Yet to find out.
Quote:
 Originally Posted by InkSprite It is continuous if you can simplify each attraction down to a 2 body system. Rotation doesn't change anything.
What does that have to do with it?

 Tags nbody, problem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Loren Physics 18 March 16th, 2017 02:15 AM szz Physics 4 September 22nd, 2015 04:20 PM spacey Physics 16 April 16th, 2013 10:06 AM shyronnie Physics 9 April 9th, 2012 11:38 PM r-soy Calculus 2 December 29th, 2010 04:37 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top