摘要
本文建立了复杂双摆的Hamiltonian运动方程,并将重力作为扰动,利用KAM理论研究了复杂双摆的运动规律.研究结果表明:复杂双摆运动规律与传统双摆运动规律类似,当重力能量与总能量相比很小时,KAM不变闭曲线存在表明无重力系统的“总动量”守恒的特点.
This paper deals with the Hamiltonian equations of the complex double pendulum.
The KAM theory can be used to study the motions of the complex double pendulum if the
gravitation is treated as a perturbation. The studied result shows that the motions of the
complex double pendulum are similar to the motions of the traditional double pendulum, and
the existence of KAM invariant closed curves expresses that some characters of the “total
generalied momentum” conservation of the gravity free system can be kept when the
gravitation energy is small in comparison with the total energy.
出处
《高校应用数学学报(A辑)》
CSCD
北大核心
1999年第2期147-154,共8页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金
博士点基金