| 复杂单摆的KAM理论 |
| |
| 引用本文： | 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. |
| |
| 作者姓名： | 梁建莉 汤龙坤 |
| |
| 作者单位： | 华侨大学,数学科学学院,福建,泉州,362021 |
| |
| 基金项目： | 国务院侨办科研基金资助项目(08QZR10) |
| |
| 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...
|
| 关 键 词： | 复杂单摆 无重力系统 KAM理论 哈密顿系统 |
KAM Theory of the Complex Pendulum |
| |
| LIANG Jian-li,TANG Long-kun.KAM Theory of the Complex Pendulum[J].Journal of Huaqiao University(Natural Science),2011,32(2):231-234. |
| |
| Authors: | LIANG Jian-li TANG Long-kun |
| |
| Institution: | LIANG Jian-li,TANG Long-kun(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China) |
| |
| 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-... |
| |
| Keywords: | complex pendulum gravity-free system KAM theory Hamiltonian system |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
