考虑轴承摩擦的复摆运动

Study of Motion of a Compound Pendulum with Accounting for the Influence of Bearing Friction

现行的许多理论力学教科书中都介绍过一个有关如何建立复摆运动微分方程的例子,然而在该例的分析和推导当中,并没有考虑轴承摩擦对复摆运动的影响。本文旨在考虑这一影响因素的基础上,建立复摆的运动微分方程,并与未考虑轴承摩擦影响的复摆运动微分方程进行比较。最后,分别对考虑和不考虑轴承摩擦的两种情形下的复摆运动进行数值仿真,通过对仿真结果的比较,说明了上述两种情形下复摆运动的不同之处。

In many current textbooks on theoretical mechanics, an example of establishing differential equation of motion of a compound pendulum is presented. In this example, however, the influence of bearing friction on motion of the compound pendulum is not taken into consideration. In the present paper, taking into account the influence of bearing friction, the differential equation of motion of a compound pendulum is derived and compared with that without accounting for the influence of bearing friction. Based on these equations, the motion responses of a compound pendulum with and without accounting for the influence of bearing friction are numerically simulated. Finally, the difference between the motion responses is shown.