复杂双摆的KAM定理

KAM THEORY OF THE COMPLEX DOUBLE PENDULUM

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.