Author:
J. Závoti Hungarian Academy of Sciences Research Centre for Astronomy and Earth Sciences Csatkai u. 6-8 H-9400 Sopron

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The laws of nature in general, and the relations and laws in geodesy in particular can be expressed in most cases by nonlinear equations which are in general solved by transforming them to linear form and applying iteration. The process of bringing the equations to linear form implies neglections and approximation. In certain cases it is possible to obtain exact, correct solutions for nonlinear problems. In the present work we introduce parameters into the rotation matrix, and using this we derive solutions for the 2D and 3D similarity transformations. This method involves no iteration, and it does not require the transformation of the equations to linear form. The scale parameter is determined in both cases by solving a polynomial equation of second degree. This solution is already known, but our derivation is worth consideration because of its simple nature.

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Acta Geodaetica et Geophysica
Language English
Size B5
Year of
Foundation
2013
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó Springer
Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2213-5812 (Print)
ISSN 2213-5820 (Online)

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