受迫摆方程与准沟道辐射的稳定性

Forced Pendulum Equation and The Stability of Quasichannel Radiations

从受迫摆方程出发导出了系统的频率响应,并从Mathieu方程的稳定区和不稳定区讨论了系统的稳定性。指出了粒子的准沟道运动可以用周期转动解来描述,并利用系统的周期倍分叉、跳跃现象和弛豫行为讨论了准沟道粒子运动的稳定性。结果表明,适当选择参数,系统的稳定性是可以保证的。

The frequency response of the system was derived from the forced pendulum equation,and the stability of the system was discussed from the stability and instability of Mathieu equation.It is pointed out that the quasi-channel motion of particles can be described by the rotational periodic solution,and the stability of quasi-channel particle motion is discussed by using the periodic bifurcation,jumping phenomenon and relaxation behavior of the system.The results show that the stability of the system can be ensured by choosing the parameters properly.