| 保守双摆的不可积性和混沌 |
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| 引用本文： | 凌复华,徐如进.保守双摆的不可积性和混沌[J].应用数学和力学,1992,13(1):45-52. |
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| 作者姓名： | 凌复华 徐如进 |
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| 作者单位： | 上海交通大学工程力学系 |
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| 基金项目： | 国家教委博士点科研基金资助项目 |
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| 摘 要： | 本文用Birkhoff级数正则变换方法求出保守双摆运动方程的近似积分,并把近似积分的等值曲线与数值仿真结果作了比较.由此清楚地看出.当能级提高时,系统由近可积的成为不可积的,即其运动情况由规则的转变为混沌的.本文还介绍了演示上述性态的一个保守双摆模型.
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| 关 键 词： | 保守双摆 不可积性 混沌 正则变换 数值仿真 Birkhoff级数 |
| 收稿时间： | 1991-03-04 |
Non-lntegrability and Chaos of a Conservative Compound Pendulum |
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| Ling Fu-hua Xu Ru-jin.Non-lntegrability and Chaos of a Conservative Compound Pendulum[J].Applied Mathematics and Mechanics,1992,13(1):45-52. |
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| Authors: | Ling Fu-hua Xu Ru-jin |
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| Affiliation: | Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai |
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| Abstract: | By using a series of canonical transformations (Birkhoff's series), an approximate integral of a conservative compound pendulum is evaluated. Level lines of this approximate integral are compared with the numerical simulation results. It is seen clearly that with a raised energy level, the nearly integrable system becomes noh-integrable,i.e. the regular motion pattern changes to the chaotic one. Experiments with such a pendulum device display the behavior mentioned above. |
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| Keywords: | conservative compound pendulum non-integrability chaos canonicaltransformation numerical simulation Birkhoff's series normal form nth-fold resonance |
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