摘要
大学物理课程中对含钢索类约束的质点动力学问题均未考虑滑动摩擦的影响,主要原因在于由此导出的方程具有非线性特征,普遍认为不易求解。本文首先证明了当约束体为二次型曲线时,原切向方程可化为以分离变量求解的形式;然后针对一般的情形,给出了线性化的办法,导出了一阶线性非齐次常微分方程,并给出解的积分表达式。最后以一具体问题为例进行计算,对比了两种办法的特点,讨论了摩擦力的影响。
The particle dynamics of the steel cable constraints in college physics courses do not consider the influence of sliding friction.The main reason is that the resulting equations present nonlinear characteristics,which generally is not easy to solve.The paper proves that when the constraint body is two times curve,the original tangent equation can be changed into the form of the solution by separation variables.Then,for the general situation,the linearization method is given,the first order linear non-homogeneous ordinary differential equation is derived,and the integral expression of the solution is given.Finally,a specific problem is taken as an example to calculate.The characteristics of the two methods are compared and the influence of friction is discussed.
作者
何健
HE Jian(School of Mathematics and Physics,Mianyang Normal University,Mianyang Sichuan 621000)
出处
《物理与工程》
2019年第3期47-51,共5页
Physics and Engineering
基金
绵阳师范学院2018教研教改课题(Mnu-JY18159)
关键词
非线性
自然坐标系
约束体
分离变量法
nonlinear
natural coordinates
constrained body
separation of variables
