Generally speaking, the three body problem is unsolvable. See http://plus.maths.org/issue6/xfile/index.html and http://en.wikipedia.org/wiki/N-body_problem. However, in practice the problem is soluble by theories of perturbation. It is solved for some special cases in which the mass undergoes a reversal to infinitely small as in the Lagrangian and Eulerian cases.
Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c˛
three bodies meld into one. -
03-10-2006, 01:28 PM
Antonio the solution to the three body problem is simple if you think about it!
The confusion lies in creating a complexity when there is not one present.
There is in effect just "one body"=energy.which may appear to be masquer-
ading as three,but thats it it only "appears"it is an illusion,Houdini would have
liked this three bodied problem,he apparently was a master illusionist!Science
can sometimes be strangled by its own constraints,and be very closed to other ideas,that may assist them.
kind regards michael,
Humilty,coupled with boldness,surprises truth to
reveal herself?
Everybody was given a problem to solve. Somebody thought anybody can solve it. Anybody thought nobody will solve it. So nobody solves the problem what anybody could have solved.
Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c˛
As I understand it, the problem was that of a missing probe. Based on the knowledge derived from Lagrange theory and of course the direction and velocity of the probe itself it did eventually reveal itself in the predicted location and has since become a resounding success, far exceeding its life expectancy.
If the unsolvability of the problem is related to the degree of precision that pure mathematics can provide us with, how do you view the success of the Deep Impact probe? After all, it initially missed the comet Temple 1 by seven kilometers. Considering the percentage of error that that represents with respect to the distances involved I would say that was an excellent shot.
Furthermore, if the determination of the Langragian points were what ultimately led to its discovery then the math can be considered to have worked. As with any problem though, when one introduces a random factor by removing the variables of direction and velocity, then of course no true determination can be made.
three bodies meld into one. -
03-10-2006, 01:28 PM
"There is nothing permanent except change" 
Linear Mode
