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| | 已由Lincent审校。 | | 已由Lincent审校。 |
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| − | In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.[1] The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.
| + | 在物理学和经典力学领域中，'''三体问题 Three-body problem'''是根据牛顿运动定律和牛顿万有引力定律按照三点处质量体的初始位置和速度（或动量）求出它们随后的运动的问题。<ref name="PrincetonCompanion">{{Citation |
| | + | | last = Barrow-Green |
| | + | | first = June |
| | + | | year = 2008 |
| | + | | title = The Three-Body Problem |
| | + | | editor-last1 = Gowers |
| | + | | editor-first1 = Timothy |
| | + | | editor-last2 = Barrow-Green |
| | + | | editor-first2 = June |
| | + | | editor-last3 = Leader |
| | + | | editor-first3 = Imre |
| | + | | encyclopedia = The Princeton Companion to Mathematics |
| | + | | pages = 726–728 |
| | + | | publisher = Princeton University Press |
| | + | }}</ref> 三体是N体问题中的一个特例。与双体问题不同的是，三体问题不存在一般的闭式解，<ref name="PrincetonCompanion"/>因为产生的动力系统对于大多数初始条件来说是混沌的，所以一般需要数值方法求解。 |
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| − | 在物理学和经典力学领域中，三体问题是根据牛顿运动定律和牛顿万有引力定律按照三点处质量体的初始位置和速度（或动量）求出它们随后的运动的问题。三体是N体问题中的一个特例。与双体问题不同的是，三体问题不存在一般的闭式解，因为产生的动力系统对于大多数初始条件来说是混沌的，所以一般需要数值方法求解。
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| − | Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, and the Sun.[2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles.
| + | 历史上看，第一个被拓展研究的特定三体问题是月球、地球和太阳构成的“三体”问题。<ref name="first">{{cite web |url=http://www.wolframscience.com/reference/notes/972d |title=Historical Notes: Three-Body Problem |access-date=19 July 2017}}</ref>从现代意义上讲，拓展的三体问题可以是经典力学或量子力学中模拟三个粒子运动的任何问题。 |
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| − | 历史上看，第一个被拓展研究的特定三体问题是月球、地球和太阳构成的“三体”问题。从现代意义上讲，拓展的三体问题可以是经典力学或量子力学中模拟三个粒子运动的任何问题。
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| | ==数学描述== | | ==数学描述== |
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| | 这种情况下，<math>\mathcal{H}</math>仅仅是系统的总能量，重力加上动能。 | | 这种情况下，<math>\mathcal{H}</math>仅仅是系统的总能量，重力加上动能。 |
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| | ==受限制的三题问题== | | ==受限制的三题问题== |