椭圆积分在航海中的应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-09-01 DOI:10.1017/S037346332200042X

Miljenko Petrović

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引用次数: 0

摘要

在航海导航中，如果不考虑地球的扁率，则球面给出了任意两点之间的航向和距离的相对简单的解。使用一分弧的跨度等于海里的导航球。这种方法的主要缺陷是缺乏一个考虑地球偏心率的封闭公式。考虑到地球是一个扁球体，即一个具有小扁平度的旋转椭球体，计算子午弧长度的问题导致了对椭圆积分的理解。本文利用第一类、第二类和第三类不完全椭圆积分求任意椭圆弧。结果表明，与大地测量和降纬度相比，使用地心纬度具有优势。

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Application of elliptic integrals in marine navigation

Abstract If the Earth's oblateness is neglected in marine navigation, then the sphere gives a relatively simple solution for course and distance between any two points. The navigation sphere where a span of one minute of arc is equal to nautical mile is used. The primary deficiency of this approach is the lack of a closed-form formula that takes the Earth's eccentricity into account. Considering the Earth as an oblate spheroid, i.e., a rotational ellipsoid with a small flattening, the problem of computing the length of the meridian arc leads to the understanding of elliptic integrals. In this paper, incomplete elliptic integrals of the first, second and third kind are used to find an arbitrary elliptical arc. The results prove an advantage of using geocentric latitude compared to geodetic and reduced latitude.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.