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利用Melnikov方法讨论了非谐激励系统的混沌行为,并在极限情况κ→0下,把非谐激励转化为谐波激励,而运动方程化为倒置摆方程。倒置摆方程描写了带电粒子在周期弯晶中翻越势垒的横向运动行为。结果表明:系统的稳定性与参数有关,适当调整参数就能保证系统是稳定的;即使保持参数不变,调整系统初始状态也可以使系统完成从无序向有序,或者从有序向无序转换。
The Melnikov method is used to discuss the chaotic behavior of anharmonic excitation system. In the limit condition κ → 0, the non-harmonic excitation is converted into a harmonic excitation, while the motion equation is inverted pendulum equation. Inverted pendulum equations describe the lateral movement behavior of charged particles crossing barrier in cyclic bending. The results show that: the stability of the system is related to the parameters, the parameters can be adjusted properly to ensure that the system is stable; even if the parameters are kept unchanged, adjusting the initial state of the system can also make the system complete from disorder to order or from ordered to no Sequence conversion.