| The parametric orbits and the form invariance of three-body in one-dimension |
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| 作者姓名： | 楼智美 |
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| 作者单位： | Department of Physics, Shaoxing College of Arts and Sciences,Shaoxing,312000, China |
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| 摘 要： | In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces(“centrifugal potential”) in addition to linear forces (“harmonical potential”) are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H1 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied.
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| 关 键 词： | 三体运动 参数轨道 汉密尔顿函数 数量守恒 |
| 收稿时间： | 2004-10-10 |
The parametric orbits and the form invariance of three-body in one-dimension |
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| Lou Zhi-Mei.The parametric orbits and the form invariance of three-body in one-dimension[J].Chinese Physics B,2005,14(4):660-662. |
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| Authors: | Lou Zhi-Mei |
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| Institution: | Department of Physics, Shaoxing College of Arts and Sciences,Shaoxing,312000, China |
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| Abstract: | In this paper, the differential equations of motion of a three-body interacting pairwise by inverse cubic forces (``centrifugal potential') in addition to linear forces (``harmonical potential') are expressed in Ermakov formalism in two-dimension polar coordinates, and the Ermakov invariant is obtained. By rescaling of the time variable and the space coordinates, the parametric orbits of the three bodies are expressed in terms of relative energy H11 and Ermakov invariant. The form invariance of the transformations of two conserved quantities are also studied. |
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| Keywords: | three-body parametric orbits Ermakov invariant Hamiltonian function conserved quan-tities form invariance |
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