【摘要】 在牛顿力学框架内和小振幅近似下,把非相对论粒子在时空周期场中的运动方程化为含有阻尼项和受迫项的Duffing方程。利用多尺度法分析了系统的1/3分频共振;利用Poincare方法讨论了系统的稳定性;找到了系统的临界条件;揭示了共振曲线的后弯现象;讨论了系统的跳跃现象。结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数,就可以原则上保证系统的稳定性。更多还原

【Abstract】 In the framework of Newtonian mechanics and small-amplitude approximation,the motion equation of the non-relativistic particles in a periodic potential in space and time reduced to Duffing-equation with damping and forced terms,analyzed the 1/3 frequency resonance in the system using Multi-scale method;discussed stability of the system by Poincare method;found the critical condition of the system;revealed the after back bending phenomenon of resonance curve;discussed the jump phenomenon in the system.The results showed that the critical condition of the system is relate to physical parameters,only the appropriate regulation of these parameters can in principle guarantee system stability.更多还原