The behaviour of moving points on curves: A rotating frame approach
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917451842715648 |
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| author | Han, Dong |
| author_facet | Han, Dong |
| contents | In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation. Conversely, it can also be proved that a curve can be determined by the two motions of a moving point on it, namely, linear motion and rotation. Thus, we obtain a new binary mathematical formation mechanism for curves based on the aforementioned two motions. Finally, we apply this rotating frame method to the study of the behaviour of moving points on ellipses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16076 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The behaviour of moving points on curves: A rotating frame approach Han, Dong Differential Geometry In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation. Conversely, it can also be proved that a curve can be determined by the two motions of a moving point on it, namely, linear motion and rotation. Thus, we obtain a new binary mathematical formation mechanism for curves based on the aforementioned two motions. Finally, we apply this rotating frame method to the study of the behaviour of moving points on ellipses. |
| title | The behaviour of moving points on curves: A rotating frame approach |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.16076 |