Go Back   Science Forums Biology Forum Molecular Biology Forum Physics Chemistry Forum > General Science Forums > Physics Forum
Register Search Today's Posts Mark Forums Read

Physics Forum Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


N-body problem

N-body problem - Physics Forum

N-body problem - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


Reply
 
LinkBack Thread Tools Display Modes
  #1  
Old 12-01-2003, 04:33 AM
Torstein Raanes
Guest
 
Posts: n/a
Default N-body problem



Hello

Abstract:
The N-body problem looks into solving the gravity effect on all
bodies in a system most effectively.

My problem:
To get to the solution, I have to calculate the center of gravity
in a given section of the problem area that will represent all
bodies as one. This will be solved in two dimensions. All
bodies have a mass, and a position with x, y coordinates.
Could someone help me with the formula to find this point? Also
the gravity force for this point would help (and I would imagine
it is necessary to find the solution.)

Regards,
Torstein Raanes
Reply With Quote
  #2  
Old 12-01-2003, 10:31 AM
tadchem
Guest
 
Posts: n/a
Default N-body problem


"Torstein Raanes" <[Only registered users see links. ].uit.no> wrote in message
news:bqega8$2p5f$[Only registered users see links. ].no...

In a Cartesian coordinate system, the coordinates of the center of mass of a
group of point masses is the *weighted* average of the coordinates of the
individual masses. In two dimensions:

X-bar = Sum[m(i)*x(i)]/Sum[m(i)]

and

Y-bar = Sum[m(i)*y(i)]/Sum[m(i)]


Again, outside the circumscribing sphere, the collection can be treated as a
single body with

m(tot) = Sum[m(i)]

The difficulty with the N-body problem is that there are more momenta to be
conserved than there are degrees of geometric freedom, so separation of
variables into orthonormal coordinates is not possible in general. In the
two-body problem we get a solution by transforming the x, y, and z
coordinates of two bodies into six *new* coordinates with orthogonal
momenta: the x, y, and z momenta of the center of mass and the r, theta, and
z momenta (cylindrical coordinates) of the rotating binary. With only three
bodies you get nine momenta to be conserved, and it is not easy to find
places in 3 dimensions to put 9 orthogonal momenta.

Sometimes a three body problem can "rearrange" itself into two two-body
problems by "ejecting" one body leaving the other two as a binary. Then the
ejected body and the binary become an effectively independent two-body
problem.


Tom Davidson
Richmond, VA


Reply With Quote
Reply

Tags
nbody , problem


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
SDS-PAGE problem Steve Nothwehr Protocols and Methods Forum 2 10-16-2009 08:59 AM
Unidentified problem with low concentrated samples ggerard Western Blot Forum 3 12-22-2008 05:52 PM
Curvature cancelation in two body problem DougC Physics Forum 0 07-03-2008 08:49 PM
FFiMP: Misconceptions about Special Relativity Jan Gooral Physics Forum 0 05-22-2008 02:53 PM


All times are GMT. The time now is 11:23 PM.


Powered by vBulletin® Version 3.8.4
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
Copyright 2005 - 2012 Molecular Station | All Rights Reserved
Page generated in 0.12519 seconds with 16 queries