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dc.contributor.authorTatsuno, Tadao
dc.date.accessioned2020-02-06T10:56:43Z
dc.date.available2020-02-06T10:56:43Z
dc.date.issued1989
dc.identifier.urihttp://hdl.handle.net/1834/16113
dc.description.abstractMany solutions have been submitted for the first and second problem of geodesy. Among them are the solutions by Legendre, Schreiber, Gauss and Helmert. Almost all of them employ the method of series expansion of Taylor or Mclaurin. In this report, another method is employed for solution of the problem of geodesy. It is the method of numerical integral by formula of Gauss. The formulae of numerical integral are directly reduced from the Euler’s equation of the calculus of variations. Characteristic features of these two methods can be summarized as follows: Features of the method of series expansion: Higher terms of the expansion must be omitted. The omission will cause an error in the computation of azimuth, distance and position coordinates, especially in the case of long distance. Much effort is needed for expanding the formula which is satisfactorily accurate for long distance On the other hand, repeated computation is not necessary. In the days of manual calculation, this last item should have been a very good merit for practical surveyors. Features of the method of numerical integral: There is no omission of computation as in the case of series expansion. Constants of the computation of the Gaussian numerical integral can be easily obtained to any accuracy. Repeated computation is terminated by comparing with a given small positive number. This number can be given to the program without any limit, so there is no cause of error in the termination of repeated computation. Formulae of the computation are presented in eqs (9), (10), (13) and (14) for longitude and distance Results are presented in Table 5 and 6. The results are compared with the results of series expansion in Table 1, which is taken from the report of Dr Shinzi.en_US
dc.language.isojaen_US
dc.relation.urihttps://www1.kaiho.mlit.go.jp/GIJUTSUKOKUSAI/KENKYU/report/rhr25/rhr25-07.pdfen_US
dc.titleComputation of geodesics by integral method.en_US
dc.typeJournal Contributionen_US
dc.bibliographicCitation.issue25en_US
dc.bibliographicCitation.titleReport of Hydrographic and Oceanographic Researchesen_US
dc.description.statusPublisheden_US
dc.format.pagerangepp.165-179en_US
dc.type.refereedRefereeden_US
refterms.dateFOA2021-01-30T18:48:36Z


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