非平行摆线三线摆振动周期的非线性解

Nonlinear Solutions to Vibration Period of Trilinear Pendulum with Non-parallel Wires

通过下悬盘一挂点的几何约束方程,建立了非平行摆线三线摆无阻尼自由振动的二阶变系数非线性微分方程,利用该方程导出了非线性振动周期的表达式,对长、短摆线可分别用第一类和第二类椭圆积分表示.系统研究了摆长和摆角对振动周期的影响,并与线性振动的周期进行了比较,对影响短摆线测量周期的因素进行了分析.

The differential equation of nonlinear vibration for trilinear pendulum was derived the geometric constraint equation of a suspension point on the lower suspension disk. Nonl solutions to the vibration period were given by elliptic integrals and were compared with the 1 from near near vibration period. Influences of geometric parameters on the vibration period were studied system- atically, including the length of string and the angular amplitude. Calculating results indicate that the measuring period of three-string pendulum is related to other factors