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.
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.
出处
《应用数学和力学》
CSCD
北大核心
1992年第1期45-52,共8页
Applied Mathematics and Mechanics
基金
国家教委博士点科研基金资助项目
关键词
保守双摆
不可积性
混沌
正则变换
conservative compound pendulum, non-integrability, chaos, canonicaltransformation, numerical simulation, Birkhoff's series, normal form,nth-fold resonance
