“Angular eccentricity”的意思、由来-开放百科全书

Angular eccentricity is one of many parameters which arise in the study of the ellipse or ellipsoid. It is denoted here by α (alpha). It may be defined in terms of the eccentricity, e, or the aspect ratio, b/a (the ratio of the semi-minor axis and the semi-major axis):

Angular eccentricity is not currently used in English language publications on mathematics, geodesy or map projections but it does appear in older literature.^[1]

Any non-dimensional parameter of the ellipse may be expressed in terms of the angular eccentricity. Such expressions are listed in the following table after the conventional definitions.^[2] in terms of the semi-axes. The notation for these parameters varies. Here we follow Rapp:^[2]

The alternative expressions for the flattenings would guard against large cancellations in numerical work.

References

1. ^{{cite book |authorlink=Charles Haynes Haswell | last = Haswell | first = Charles Haynes | url =https://books.google.com/books?pg=PA381&id=Uk4wAAAAMAAJ#v=onepage&f=true|title = Mechanics' and Engineers' Pocket-book of Tables, Rules, and Formulas |publisher = Harper & Brothers | year = 1920 | accessdate = 2007-04-09}}
2. ^¹Rapp, Richard H. (1991). Geometric Geodesy, Part I, Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio.

External links

[https://web.archive.org/web/20070401052928/http://www.oc.nps.navy.mil/~garfield/ellipse_app2.pdf Toby Garfield's APPENDIX A: The ellipse] [https://web.archive.org/web/20070401052928/http://www.oc.nps.navy.mil/~garfield/ellipse_app2.pdf [Archived copy].]

[https://web.archive.org/web/20070928080949/http://www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf Map Projections for Europe (pg.116)]

2 : Geodesy|Conic sections