复杂单摆的KAM理论  

KAM Theory of the Complex Pendulum

作　　者：梁建莉[1] 汤龙坤[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2011年第2期231-234,共4页Journal of Huaqiao University(Natural Science)

基　　金：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.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.

关 键 词：复杂单摆 无重力系统 KAM理论 哈密顿系统 

分 类 号：O317[理学—一般力学与力学基础] O175.13[理学—力学]