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| The three-body motions with zero angular momentum is restricted to be the planar motion.
The equal mass three-body figure eight choreography which was found by Moore, Chenciner and Montgomery is one of the three-body planar motions. The figure eight choreography follows that the three tangent lines from the three bodies meet at a point (infinity is allowed)
at any time. Actually, this property holds for any zero-angular momentum
three-body motion and we can show that "If the linear momentum and the angular momentum are zero in the three-body motion, three-tangent lines meet at a point or three tangent lines are parallel."
About ten years ago, this was proved by Fujiwara, Fukuda, and Ozaki, and they called it three-tangents theorem. The three-tangent theorem can be extended to the three-body motion with non-vanishing constant angular momentum in 3 dimension. If we project three tangent lines into any plane parallel to the total angular momentum, the projected three tangent lines intersect with each other at a point or three tangent lines are parallel. The proof will be given in this talk, and we will show an example. |
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