My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Thanks Tree2Thanks
  • 1 Post By Micrm@ss
  • 1 Post By SDK
Reply
 
LinkBack Thread Tools Display Modes
June 24th, 2018, 02:09 PM   #1
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 390
Thanks: 27

Math Focus: Number theory
Path of 3 bodies in a plane...

Can an exact solution be found for the trajectories of three point-like particles, of unspecified but nonzero mass, gravitating together but confined to a plane?

Can the general three-body problem be solved exactly for any interaction; e.g., by any central force, where one body is a massive horizon?
Loren is offline  
 
June 25th, 2018, 02:01 AM   #2
Senior Member
 
Joined: Oct 2009

Posts: 608
Thanks: 186

Quote:
Originally Posted by Loren View Post
Can an exact solution be found for the trajectories of three point-like particles, of unspecified but nonzero mass, gravitating together but confined to a plane?
Not in general, although very specific cases can be known.
Thanks from Loren
Micrm@ss is offline  
June 25th, 2018, 05:42 PM   #3
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 500
Thanks: 277

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
Originally Posted by Micrm@ss View Post
Not in general, although very specific cases can be known.
This isn't really true. This is commonly referred to as the "3 body problem" in general or often the "circular restricted" 3 body problem. The vector field associated with it is analytic and Hamiltonian for all values of the masses so it admits a perfectly good solution for any (non-collision) initial conditions and these solutions are perfectly easy to compute.

Perhaps the misunderstanding is due to the fact that the 3 body problem is NOT integrable? This isn't true for the 2 body (Kepler) problem which is always integrable. However, this result doesn't mean the 3 body problem has no solutions or that they can't be computed. It says the solutions aren't "nice" (the solution curves aren't restricted to invariant tori).
Thanks from Loren
SDK is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
bodies, path, plane



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find all points on surface whose tangent plane is parallel to given plane Addez123 Calculus 4 November 12th, 2016 07:51 AM
2 Points in R3 and 1 point on plane. How to find equation of plane? extreme112 Linear Algebra 2 October 13th, 2015 08:34 AM
path dependent function with a definite path aise5668 Real Analysis 3 March 5th, 2012 07:36 PM
Calculate the inertia tensor for two rigid bodies? mrbiggl3s Calculus 1 September 29th, 2011 10:19 AM





Copyright © 2018 My Math Forum. All rights reserved.