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

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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.

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