Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields
The differential geometry of plane curves has many applications in physics especially in mechanics. The curvature of a plane curve plays a role in the centripetal acceleration and the centripetal force of a particle traversing a curved path in a plane. In this paper, we introduce the concept of the...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/9881237 |
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| _version_ | 1832562308517199872 |
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| author | Azeb Alghanemi Abeer AlGhawazi |
| author_facet | Azeb Alghanemi Abeer AlGhawazi |
| author_sort | Azeb Alghanemi |
| collection | DOAJ |
| description | The differential geometry of plane curves has many applications in physics especially in mechanics. The curvature of a plane curve plays a role in the centripetal acceleration and the centripetal force of a particle traversing a curved path in a plane. In this paper, we introduce the concept of the f-curves associated with a plane curve which are more general than the well-known curves such as involute, evolute, parallel, symmetry set, and midlocus. In fact, we introduce the f-curves associated with a plane curve via its normal and tangent for both the cases, a Frenet curve and a Legendre curve. Moreover, the curvature of an f-curve has been obtained in several approaches. |
| format | Article |
| id | doaj-art-1ccb64895de24059907d71bb900907ce |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-1ccb64895de24059907d71bb900907ce2025-02-03T01:22:57ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/9881237Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector FieldsAzeb Alghanemi0Abeer AlGhawazi1Department of MathematicsDepartment of MathematicsThe differential geometry of plane curves has many applications in physics especially in mechanics. The curvature of a plane curve plays a role in the centripetal acceleration and the centripetal force of a particle traversing a curved path in a plane. In this paper, we introduce the concept of the f-curves associated with a plane curve which are more general than the well-known curves such as involute, evolute, parallel, symmetry set, and midlocus. In fact, we introduce the f-curves associated with a plane curve via its normal and tangent for both the cases, a Frenet curve and a Legendre curve. Moreover, the curvature of an f-curve has been obtained in several approaches.http://dx.doi.org/10.1155/2022/9881237 |
| spellingShingle | Azeb Alghanemi Abeer AlGhawazi Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields Advances in Mathematical Physics |
| title | Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields |
| title_full | Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields |
| title_fullStr | Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields |
| title_full_unstemmed | Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields |
| title_short | Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields |
| title_sort | some geometric characterizations of f curves associated with a plane curve via vector fields |
| url | http://dx.doi.org/10.1155/2022/9881237 |
| work_keys_str_mv | AT azebalghanemi somegeometriccharacterizationsoffcurvesassociatedwithaplanecurveviavectorfields AT abeeralghawazi somegeometriccharacterizationsoffcurvesassociatedwithaplanecurveviavectorfields |