Mathematical models transformations of spatial coordinates

Geodesy

UDC:

528.2

DOI:

10.22389/0016-7126-2016-909-3-2-7

1 Medvedev P.A.

Year:

2016

№:

909

Pages:

2–7

Omsk State Agrarian University named after P.A. Stolypin

1,

Abstract:

Mathematical models transformations of coordinates used for solution of geodetic tasks in the space are analysed. Analyses of algorithms recommended in State Standards of the Russian Federation, transformations of spatial rectangular geocentric coordinates in prescribed system of reading in spatial geodetic coordinates are carried out. Defects of the mathematical solutions of this task are pointed out and simple algorithms for determination of geodetic latitude and longitude are given. The formulas of the rectangular spatial coordinates connections with polar spherical coordinates are investigated. Dependence with half argument usage is also obtained for calculation of geocentric latitude. The systems of topocentric horizontal coordinates are analyzed by the same method. Optimal algorithms for calculation of zenithal distance and geodetic azimuth are suggested according to the results of investigations. All suggested algorithms do not require the additional researches for determination of unknown quantities according to the meanings of trigonometrical functions.

Keywords:

transformation of сoordinates, rectangular coordinates, geodetic coordinates, polar coordinates

References:

1. Bojko E.G. Vysshaya geodeziya: Ch. II. Sferoidicheskaya geodeziya. M.: Kartgeocentr – Geodezizdat, 2003, 144 p.

2. Mashimov M.M. Geodeziya: Teoreticheskaya geodeziya. M.: Nedra, 1991, 268 p.

3. Sistema geodezicheskih parametrov Zemli «Parametry Zemli 1990 goda» (PZ-90). Pod obshch. red. V.V. Hvostova. M.: Koordinacionnyj nauch.-inform. centr, 1998, 40 p.

4. Medvedev P.A. (1994) Investigation of recurrence formulas for calculating latitude in the transition from spatial rectangular coordinates to geodetic. Geodesy and Cartography, 55(6), pp. 8–14.

5. Medvedev P.A. Analiz preobrazovanij prostranstvennyh pryamougol'nyh koordinat v geodezicheskie. Omsk: izd. OmGAU, 2000, 104 p.

6. Medvedev P.A. (2014) The analyses of transformation of the spatial coordinates of ground points. Geodezia i Kartografia, (4), pp. 2-8. (In Russian). DOI: 10.22389/0016-7126-2014-886-4-2-8.

7. Morozov V.P. Kurs sferoidicheskoj geodezii. Izd. 2-e, pererab. i dop. M.: Nedra, 1979, 295 p.

8. Nasibullin A.Yu. Novyj algoritm resheniya geodezicheskih zadach v prostranstve. Geodezist, 2002, no. 2, pp. 10–11.

9. Ogorodova L.V. Vysshaya geodeziya. Chast' III. Teoreticheskaya geodeziya: Ucheb. dlya vuzov. M.: Geodezkartizdat, 2006, 384 p.

10. Penev P., Peneva E. Preobrazovanie pryamougol'nyh geocentricheskih koordinat v geodezicheskie bez primeneniya iteracij. Izv. vuzov. Geodeziya i aehrofotos"emka, 2012, no. 3, pp. 34–38.

11. Urmaev M.S. Kosmicheskaya fotogrammetriya. M.: Nedra, 1989, 279 p.

Citation:

Medvedev P.A.,

(2016) Mathematical models transformations of spatial coordinates. Geodesy and cartography = Geodezia i Kartografia, (3), pp. 2–7. (In Russian). DOI: 10.22389/0016-7126-2016-909-3-2-7

Refbacks:

Ogorodova L.V. (2017) Reliable and easy method for converting geodetic rectangular coordinates into curvilinear ones. Geodesy and Cartography = Geodezia i kartografia, (1), pp. 2-6. (In Russian). DOI: 10.22389/0016-7126-2017-919-1-2-6.

Afonin K.F. (2021) The method of using differential amendments to convert spatial rectangulars coordinates into those geodesic ones. Geodesy and Cartography = Geodezia i kartografia, 82 (4), pp. 2-7. (In Russian). DOI: 10.22389/0016-7126-2021-970-4-2-7.

Publication History

Received: 03.02.2015

Accepted: 18.11.2015

Published: 20.04.2016