非对称三线摆模型研究

Modeling of the Unsymmetrical Trifilar Pendulum

三线摆是用于物体转动惯量测量的常用方法之一,现有的三线摆在应用时除了要满足小摆角条件外,还需要满足众多的对称性条件.利用带乘子的拉格朗日方程对不满足任何对称性条件的三线摆进行了研究,导出了由6个二阶常微分方程和3个代数方程组成的动力学模型.该模型可以用于估算在使用传统三线摆时由于对称性偏离而带来的转动惯量的测量误差,也为拓展三线摆的应用范围打下了理论基础.

rifilar pendulum is one of the commonly used methods for measuring the moment of inertia （MOI）. The existing trifilar pendulum works under small angle condition and certain geometrically symmetrical condi- tions. By using Lagrang＇s Equation with multipliers, the unsymmetrical trifilar pendulum that was free from the above mentioned conditions was investigated, of which the dynamic model was derived as a composition of six second order ODEs and three algebraic equations. The model can be used to evaluate the measurement er- ror of MOI caused by the deviation of symmetrical conditions in the traditional trifilar pendulum, and lay a theoretical foundation in expanding the application area of trifilar pendulum.