摘要
在质点所受的作用力为线性变化的情形下,当初始时刻作用力、末端时刻作用力与时间间隔上总位移三者不在同一平面时,质点运动轨迹必为空间挠曲线和正则的简单曲线,否则,必为平面曲线,且曲率和挠率处处不等于零。当质点运动轨迹为平面曲线时,给出了质点的运动轨迹曲线,有尖点、拐点和自交点的条件,并讨论了相关的性质,这些性质在几何上是直观的。
On the condition of linear change of particle＇s acting force, it is proved that the motion trajectory of particle must be a spatial curve and a simple regular curve when the initial acting force, the terminal acting force and total displacement in the time interval not located in the same plane; otherwise, it must be a planar curve, and its curvature and its torsion at any point doesn＇t equal to zero respectively. As the motion trajectory is a planar curve, the conditions are given, where it has cusp, inflection and self-intersection recpectively. Some related properties are investigated, all of them are intuitive in geometry.
出处
《计算力学学报》
EI
CAS
CSCD
北大核心
2010年第2期347-351,共5页
Chinese Journal of Computational Mechanics
基金
陕西省自然科学研究计划(2000SL08)资助项目
