| 赵红星,叶正麟.线性力下质点运动轨迹的几何分析[J].计算力学学报,2010,27(2):347~351 |
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| 线性力下质点运动轨迹的几何分析 |
| Geometrical analysis on motion trajectory of particle under linear force |
| 投稿时间：2008-03-14 |
| DOI：10.7511/jslx20102029 |
| 中文关键词: 线性力 轨迹曲线 尖点 拐点 自交点AMS(2000)15A06 |
| 英文关键词:linear force trajectory of particle cusp inflection self-intersection |
| 基金项目:陕西省自然科学研究计划(2000SL08)资助项目. |
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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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. |
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