I'm looking for a proof, which shows that "the 3-body-problem" in physics is mathematically unsolvable.
Does anyone know some URLs that contain a proof in mathematical detail?
You know, in Astrodynamics, this problem is famous as an extension of Kepler problem or two-body-problem.
It says that we can solve equations of 2 bodies, such as the motions of earth and moon.
But when it comes to 3 objects, we can NOT solve equations about these three. Analytically, we can't get the solution.
Why is that impossible?
Related keywords are here:
(1) In 3-body-problem, there's a lack of "first-integral" (conservatives).
(2) This matter is related to system of "integrable systems".
(3) This matter is also related to "differential Galois Theory". because motions are described by differential equations.
(When we want to prove that some equations are unsolvable in algebra, Galois Theory is a useful tool. And differential Galois Theory is higher concept.)
(4) In some special conditions, 3-body-problem is solvable. For example, they have solutions such that 3 objects are on one line, or 3 objects draws a shape like "8".
But it's just in a special conditions. Generally, 3-body-problem is unsolvable. I am talking about the general case.
I can not find any specific proof about this problem, though it's very important well-known result of science...
Where on the www can I see the mathematical proof? Thanks in advance.
