摘要
应用自然坐标系中的动力学方程逐步推导出粗糙斜面上滑块平抛运动的速率、坐标、运动时间随角度φ的变化函数,也即滑块的含参运动学方程和含参轨迹方程,并作出不同情形也即不同的斜面倾角下滑块的等时逐点轨迹图。文章详细分析了滑块的速率、速度分量,以及不同情形下的运动状况,给出斜面倾角较大时滑块在水平方向能够滑至∞远的数学原因,由此揭示出雨天汽车在下坡时极易侧滑的力学机制。此外,文章对特殊情况下滑块解析形式的轨迹方程和运动方程等进行了系统的讨论。另外,文章还指出文中选择角度φ作为积分变量的玄机所在。
In this paper,by using the dynamic equations in natural coordinate system,the functions changing with angleφof the velocity,coordinate and movement time of the slider of horizontal projectile motion on the rough inclined plane are derived step by step,that is,kinematic equation and trajectory equation of the slide with parameters,and the isochronous point by point trajectory diagrams of the slider under different circumstances,that is,different inclined angles of the inclined plane are made.The velocity and its component of the slider and the motion of the slider in different situations are analyzed in detail.The mathematical reason why the slider can slide to∞far in the horizontal direction when the slope angle is large is given.Thus,the mechanical mechanism that the vehicle is easy to slide when going downhill in rainy days is revealed.In addition,the paper systematically discusses the track equation and the motion equation of the analytical form of the slider in special cases.By the way,the paper also points out the mystery of choosing angleφas the integral variable.
作者
邵云
SHAO Yun(School of Electronic Engineering,Nanjing Xiaozhuang College,Nanjing 211171,China)
出处
《安徽师范大学学报（自然科学版）》
CAS
2020年第6期537-544,共8页
Journal of Anhui Normal University(Natural Science)
基金
江苏省教育科学"十三五"规划课题(D/2020/01/55)
南京晓庄学院优秀教学团队建设项目(4187061).
关键词
滑块
粗糙斜面
平抛运动
轨迹方程
运动方程
slider
the rough inclined plane
horizontal projectile motion
trajectory equation
kinematic equation
