能量法分析重力和点电荷双场联合作用下的微幅摆动

ON THE MICRO-AMPLITUDE VIBRATION OF A PENDULUM IN THE SIMULTANEOUS FIELD OF THE GRAVITY AND POINT CHARGE BY THE ENERGY METHOD

单摆是经典的教学案例.为了丰富教学材料,文章分析了点电荷场和重力场联合作用下的摆动.采用了适合于单自由度的自然坐标系描述系统,使用了适合于复杂力学的能量法建立动力学方程.针对固定点电荷处于摆悬挂点垂线的特殊情形,通过理论分析界定了摆球最低、倒立和倾斜等平衡位置的参数范围.

The simple pendulum is a typical teaching case.To enrich teaching materials,we studied the micro-amplitude pendulum vibration caused by the simultaneous point charge and gravity fields.The system is described by the natural coordinate system,which is apt to the single-degree-of-freedom case investigated here.The dynamics equation is evolved from the energy method,which is more concise than the free-body-diagram method for the complex system in this study.After a general analysis,we focus on a particular case wherein the point charge is at the vertical line passing through the pendulum suspension point.Theoretical analysis indicates that this particular case is characterized with three types of stable balance.The three types are the ordinary,the inverted and the oblique distinguished by the pendulum rope＇s inclination.Their parametric domains are delimited.