On Funk's parabolas
This study aims to analyze parabolas in the two dimensional unit disk equipped with a Funk metric. The analysis leads to four types of parabolas are obtained, due to the non-reversibility of the Funk metric. Each one with applications to physics in the Zermelo navigation problem. In addition, we id...
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| Format: | Article |
| Language: | English |
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Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)
2024-01-01
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| Series: | REMAT |
| Subjects: | |
| Online Access: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/6680 |
| _version_ | 1827351261073113088 |
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| author | Newton Mayer Solórzano Chávez Junior Rodrigues Moyses Víctor Arturo Martínez León |
| author_facet | Newton Mayer Solórzano Chávez Junior Rodrigues Moyses Víctor Arturo Martínez León |
| author_sort | Newton Mayer Solórzano Chávez |
| collection | DOAJ |
| description |
This study aims to analyze parabolas in the two dimensional unit disk equipped with a Funk metric. The analysis leads to four types of parabolas are obtained, due to the non-reversibility of the Funk metric. Each one with applications to physics in the Zermelo navigation problem. In addition, we identify that two of the four parabolas obtained are in well known Euclidian conics, and the remaining two are characterized by irreducible quartics.
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| first_indexed | 2024-03-08T01:59:36Z |
| format | Article |
| id | doaj.art-3c6663e0fb484ffe8ad368901af3bb3c |
| institution | Directory Open Access Journal |
| issn | 2447-2689 |
| language | English |
| last_indexed | 2024-03-08T01:59:36Z |
| publishDate | 2024-01-01 |
| publisher | Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
| record_format | Article |
| series | REMAT |
| spelling | doaj.art-3c6663e0fb484ffe8ad368901af3bb3c2024-02-14T05:36:00ZengInstituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)REMAT2447-26892024-01-0110110.35819/remat2024v10i1id6680On Funk's parabolasNewton Mayer Solórzano Chávez0Junior Rodrigues Moyses1Víctor Arturo Martínez León2Universidade Federal da Integração Latino-Americana (UNILA), Foz do Iguaçu, PR, BrasilUniversidade Federal de Goiás (UFG), Goiânia, GO, BrasilUniversidade Federal da Integração Latino-Americana (UNILA), Foz do Iguaçu, PR, Brasil This study aims to analyze parabolas in the two dimensional unit disk equipped with a Funk metric. The analysis leads to four types of parabolas are obtained, due to the non-reversibility of the Funk metric. Each one with applications to physics in the Zermelo navigation problem. In addition, we identify that two of the four parabolas obtained are in well known Euclidian conics, and the remaining two are characterized by irreducible quartics. https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/6680Finsler metricFunk metricnavigation problemFunk's parabolas |
| spellingShingle | Newton Mayer Solórzano Chávez Junior Rodrigues Moyses Víctor Arturo Martínez León On Funk's parabolas REMAT Finsler metric Funk metric navigation problem Funk's parabolas |
| title | On Funk's parabolas |
| title_full | On Funk's parabolas |
| title_fullStr | On Funk's parabolas |
| title_full_unstemmed | On Funk's parabolas |
| title_short | On Funk's parabolas |
| title_sort | on funk s parabolas |
| topic | Finsler metric Funk metric navigation problem Funk's parabolas |
| url | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/6680 |
| work_keys_str_mv | AT newtonmayersolorzanochavez onfunksparabolas AT juniorrodriguesmoyses onfunksparabolas AT victorarturomartinezleon onfunksparabolas |