Polar tangential angles and free elasticae
In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae.
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-03-01
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| Series: | Mathematics in Engineering |
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| Online Access: | http://www.aimspress.com/article/doi/10.3934/mine.2021034?viewType=HTML |
| _version_ | 1819163591317651456 |
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| author | Tatsuya Miura |
| author_facet | Tatsuya Miura |
| author_sort | Tatsuya Miura |
| collection | DOAJ |
| description | In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae. |
| first_indexed | 2024-12-22T17:46:34Z |
| format | Article |
| id | doaj.art-10ad508c008a440fa31ab0e571972565 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-22T17:46:34Z |
| publishDate | 2021-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-10ad508c008a440fa31ab0e5719725652022-12-21T18:18:16ZengAIMS PressMathematics in Engineering2640-35012021-03-013411210.3934/mine.2021034Polar tangential angles and free elasticaeTatsuya Miura0Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JapanIn this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae.http://www.aimspress.com/article/doi/10.3934/mine.2021034?viewType=HTMLpolar tangential anglemonotone curvaturefree elasticaobstacle problem |
| spellingShingle | Tatsuya Miura Polar tangential angles and free elasticae Mathematics in Engineering polar tangential angle monotone curvature free elastica obstacle problem |
| title | Polar tangential angles and free elasticae |
| title_full | Polar tangential angles and free elasticae |
| title_fullStr | Polar tangential angles and free elasticae |
| title_full_unstemmed | Polar tangential angles and free elasticae |
| title_short | Polar tangential angles and free elasticae |
| title_sort | polar tangential angles and free elasticae |
| topic | polar tangential angle monotone curvature free elastica obstacle problem |
| url | http://www.aimspress.com/article/doi/10.3934/mine.2021034?viewType=HTML |
| work_keys_str_mv | AT tatsuyamiura polartangentialanglesandfreeelasticae |