Direct transformation from geocentric coordinates to geodetic coordinates

2002 ◽  
Vol 76 (8) ◽  
pp. 451-454 ◽  
Author(s):  
H. Vermeille
Keyword(s):  
Direct Transformation ◽  
Geodetic Coordinates ◽  
Geocentric Coordinates

scholarly journals Direct transformation from Cartesian into geodetic coordinates on a triaxial ellipsoid

2020 ◽  
Vol 142 ◽  
pp. 104551 ◽  
Author(s):  
Gema Maria Diaz–Toca ◽  
Leandro Marin ◽  
Ioana Necula
Keyword(s):  
Triaxial Ellipsoid ◽  
Direct Transformation ◽  
Geodetic Coordinates

Getchell’s method for conversion of Cartesian-geocentric to geodetic coordinates – Its properties and Newtonian alternative

2021 ◽  
Vol 15 (1) ◽  
pp. 47-60
Author(s):  
Roman Kadaj
Keyword(s):  
Initial Conditions ◽  
Iterative Algorithms ◽  
Geometric Interpretation ◽  
Numerical Error ◽  
Practical Significance ◽  
Stable Form ◽  
Practical Applications ◽  
Geodetic Coordinates ◽  
Set Of Points ◽  
Geocentric Coordinates

AbstractThe paper concentrates on the iterative Getchell’s method (formulated in 1972) and its alternative Newtonian implementation for conversion of Cartesian geocentric coordinates into geodetic coordinates. The same basic equation formulated in the Getchell’s method is used in both cases. The equation has a stable form in the whole range of argument (latitude) variation \langle -\pi /2,\pi /2\rangle . The original Getchell’s method (somehow “forgotten”) has a simple geometric interpretation and its applications turn out to be particularly effective. Many studies on iterative algorithms usually omit theoretical proofs of convergence replacing them with conclusions based on numerical examples. This paper presents theoretical proofs of algorithms convergence both for the Getchell’s method and the Newton procedure. The convergence parameter and numerical error of results were estimated in each case. Numerical tests were carried out for a set of points distributed on the Earth’s space, also for extreme h values. For typical practical applications of the Getchell’s method, sufficiently accurate results are obtained after 1–3 iterations, while in the Newton procedure already after one iteration, assuming the same numerical error and initial conditions. The accuracy of the geodetic coordinates determinations meets all practical requirements with some margin. For example an absolute numerical error for latitude is approx. 0.4\cdot {10^{-13}} [rad] i. e. about 0.00026 mm in the length of the meridian arc. The proposed methods were compared with other methods (algorithms), including in terms of stability and non-singularity in the entire usable space of the Earth, but excluding the near geocenter, which has no practical significance. Both the modification of the Getchell method and its Newtonian alternative are very good determined in this area (in the Earth’s poles, the final solution is directly the starting value of iterative algorithms). The discussed algorithms were implemented in the form of procedures in DELPHI language.

Total Synthesis of (+)-Granatumine A and Related Bislactone Limonoid Alkaloids via a Pyran to Pyridine Interconversion

2019 ◽  
Author(s):  
Timothy Newhouse ◽  
Alexander Schuppe ◽  
Yizhou Zhao ◽  
Yannan Liu
Keyword(s):  
Total Synthesis ◽  
Inhibitory Activity ◽  
Knoevenagel Condensation ◽  
Cost Effective ◽  
Effective Procedure ◽  
Direct Transformation ◽  
Structural Revision ◽  
Alpha Beta ◽  
Ptp 1B

We report the first total synthesis of (+)-granatumine A, a limonoid alkaloid with PTP-1B inhibitory activity, in 10 steps. Over the course of this study, two key methodological advances were made: a cost effective procedure for ketone alpha,beta-dehydrogenation using allyl-Pd catalysis, and a Pd-catalyzed protocol to convert epoxyketones to 1,3-diketones. The central tetrasubstituted pyridine is formed by a convergent Knoevenagel condensation and carbonyl-selective electrocyclization cascade, which was followed by a direct transformation of a 2<i>H</i>-pyran to a pyridine. These studies have led to the structural revision of two members of this family.

Cyclization Dichotomy of D-xylo-Hex-5-ulosonamides and Synthesis of Piperidine Analogs of Aldohexoses and Aldohexono-1,5-lactones

1999 ◽  
Vol 64 (4) ◽  
pp. 673-684 ◽  
Author(s):  
Radka Kováříková ◽  
Miroslav Ledvina ◽  
David Šaman
Keyword(s):  
Boat Conformation ◽  
Direct Transformation

The preparation of 2,3,4,6-tetra-O-benzyl-5-D-xylo-hex-5-ulosonamides 3a and 3b and their cyclization to 5-amino-2,3,4,6-tetra-O-benzyl-5-deoxy-D-glucono-1,5-lactam (4) and 5-amino- 2,3,4,6-tetra-O-benzyl-5-deoxy-D-talono-1,5-lactam (5) or to 2,3,4,6-tetra-O-benzyl-1,5-dideoxy-1,5-imino-D-glucitol (9), and also their direct transformation into 2,3,4,6-tetra-O-benzyl- D-talono-1,5-lactone (6), are described and discussed. The atypical boat conformation of D-talonolactam 5 and D-talonolactone 6 was found.

Transition-metal-free and facile synthesis of 3-alkynylpyrrole-2, 4-dicarboxylates from methylene isocyanides and propiolaldehyde

2021 ◽  
Author(s):  
Xiaoli Huo ◽  
Xiaojuan Chen ◽  
Liya Yu ◽  
Chong Zhang ◽  
Linghui Zeng ◽  
...  
Keyword(s):  
Transition Metal ◽  
Efficient Method ◽  
Transformation Process ◽  
Facile Synthesis ◽  
Direct Transformation ◽  
Metal Free

A transition-metal-free, facile and efficient method for the synthesis of 3-alkynylpyrrole-2, 4-dicarboxylates from methylene isocyanides and propiolaldehyde with moderate to good yields has been developed. The direct transformation process and...

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