[1]梁建莉,汤龙坤.复杂单摆的KAM理论[J].华侨大学学报(自然科学版),2011,32(2):231-234.[doi:10.11830/ISSN.1000-5013.2011.02.0231]
　LIANG Jian-li,TANG Long-kun.KAM Theory of the Complex Pendulum[J].Journal of Huaqiao University(Natural Science),2011,32(2):231-234.[doi:10.11830/ISSN.1000-5013.2011.02.0231]
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复杂单摆的KAM理论()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第32卷
期数:
2011年第2期
页码:
231-234
栏目:
出版日期:
2011-03-20

文章信息/Info

Title:
KAM Theory of the Complex Pendulum
文章编号:
1000-5013(2011)02-0231-04
作者:
梁建莉; 汤龙坤
华侨大学数学科学学院
Author(s):
LIANG Jian-li;  TANG Long-kun
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
复杂单摆;  无重力系统;  KAM理论;  哈密顿系统
Keywords:
complex pendulum;  gravity-free system;  KAM theory;  Hamiltonian system
分类号:
O314
DOI:
10.11830/ISSN.1000-5013.2011.02.0231
文献标志码:
A
摘要:
建立了一类复杂单摆的运动方程.首先利用一个动量守恒的首次积分将二自由度系统转化为单自由度系统,然后利用KAM理论,将重力能量作为小扰动项,研究了复杂单摆的运动规律.研究表明:当重力能量与总能量相比很小时,或者单摆总能量充分大时,复杂单摆的KAM不变曲线仍然存在,整个系统做拟周期运动,扰动系统仍然具有无重力系统的运动规律.
Abstract:
The motions of a complex pendulum is studied in this paper.A two degrees systems is transformed into a single degree system by means of a momentum conservation.The system is studied by treating the gravitation as a small perturbation in KAM theory.It is shown that when the gravitational energy is small compared with the total energy,or the total energy is sufficiently large,there still exists the KAM invariant curves.It is also shown that the system is a quasi-periodic system and the motions of the gravity-free system can be kept to the perturbation system.

参考文献/References:

[1] 胡志兴, 管克英. 复杂双摆的KAM定理 [J]. 高校应用数学学报A辑, 1999(2):147-154.
[2] 胡志兴, 管克英. 陀螺仪运动的混沌与KAM理论 [J]. 应用数学学报, 2000(2):212-220.doi:10.3321/j.issn:0254-3079.2000.02.007.
[3] ARNOLD V I. Mathematical methods of classical mechanics [M]. New York:springer-verlag, 1978.
[4] 程崇庆, 孙义燧. 哈密顿系统中的有序和无序运动 [M]. 上海:上海科学技术出版社, 1996.

备注/Memo

备注/Memo:
国务院侨办科研基金资助项目(08QZR10)
更新日期/Last Update: 2014-03-23