摘要
运用牛顿第二运动定律对弹簧螺旋摆系统建立了模型方程,该方程为一组非线性微分方程,表明该系统具有复杂的非线性特征.理论分析表明,当系统固有的振动频率和摆动频率之比为2时,自由振动的弹簧螺旋摆系统存在内共振现象,数值求解结果证实了这一结论.并认为在一般情况下,弹簧螺旋摆系统的自由振动可能是准周期的.
The motion equations of a spring-spiral-pendulum system are derived by using the Newton＇s second law.The equations are a set of nonlinear ordinary differential equations which indicate that there exist complex dynamical structures in a spring-spiral-pendulum system.Theoretical analysis shows that there exists an internal resonance phenomenon,which is verified by the numerical results,when the system of spring-spiral-pendulum vibrating is freely.For the general case,we believe that the motion of a vibrating freely spring-spiral-pendulum is probably semi-periodic.
出处
《大学物理》
北大核心
2010年第10期3-7,共5页
College Physics
基金
教育部科学技术研究重点项目(209128)
西北师范大学科技创新工程(NWNU-KJCXGC-03-53)
西北师范大学大学生科技创新项目资助课题
关键词
弹簧螺旋摆
非线性振动
内共振
spring-spiral-pendulum
nonlinear vibration
internal resonance
