New Formulae for Combined Spherical Triangles.
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| Title: | New Formulae for Combined Spherical Triangles. |
|---|---|
| Authors: | Hsieh, Tsung-Hsuan zxxie@shmtu.edu.cn, Wang, Shengzheng, Liu, Wei, Zhao, Jiansen |
| Source: | Journal of Navigation. Mar2019, Vol. 72 Issue 2, p503-512. 10p. |
| Subjects: | Navigation, Spherical trigonometry, Mathematical formulas, Problem solving, Quadrilaterals |
| Abstract: | Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Navigation is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 134685131 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: New Formulae for Combined Spherical Triangles. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hsieh%2C+Tsung-Hsuan%22">Hsieh, Tsung-Hsuan</searchLink><i> zxxie@shmtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Shengzheng%22">Wang, Shengzheng</searchLink><br /><searchLink fieldCode="AR" term="%22Liu%2C+Wei%22">Liu, Wei</searchLink><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Jiansen%22">Zhao, Jiansen</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Navigation%22">Journal of Navigation</searchLink>. Mar2019, Vol. 72 Issue 2, p503-512. 10p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Navigation%22">Navigation</searchLink><br /><searchLink fieldCode="DE" term="%22Spherical+trigonometry%22">Spherical trigonometry</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+formulas%22">Mathematical formulas</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink><br /><searchLink fieldCode="DE" term="%22Quadrilaterals%22">Quadrilaterals</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Navigation is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1017/S0373463318000772 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 503 Subjects: – SubjectFull: Navigation Type: general – SubjectFull: Spherical trigonometry Type: general – SubjectFull: Mathematical formulas Type: general – SubjectFull: Problem solving Type: general – SubjectFull: Quadrilaterals Type: general Titles: – TitleFull: New Formulae for Combined Spherical Triangles. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hsieh, Tsung-Hsuan – PersonEntity: Name: NameFull: Wang, Shengzheng – PersonEntity: Name: NameFull: Liu, Wei – PersonEntity: Name: NameFull: Zhao, Jiansen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 03734633 Numbering: – Type: volume Value: 72 – Type: issue Value: 2 Titles: – TitleFull: Journal of Navigation Type: main |
| ResultId | 1 |
