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| Geometrical analysis on motion trajectory of particle under linear force |
| Received:March 14, 2008 |
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| DOI：10.7511/jslx20102029 |
| KeyWord:linear force trajectory of particle cusp inflection self-intersection |
| Author | Institution |
| 赵红星 |
榆林学院 数学系,榆林 71900 |
| 叶正麟 |
西北工业大学 理学院,西安 |
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| Abstract: |
| 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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