A second order Jupiter-Saturn planetary theory

1982 ◽  
Vol 27 (4) ◽  
pp. 417-430 ◽  
Author(s):  
Osman M. Kamel ◽  
Abdel Aziz Bakry
Keyword(s):  
Second Order ◽  
Planetary Theory

A Second Order Secular J–S Planetary Theory Part I : Lemma

2020 ◽  
Vol 22 (4) ◽  
pp. 871-874
Author(s):  
Osman M. Kamel ◽  
Adel S. Soliman
Keyword(s):  
Second Order ◽  
Planetary Theory

AbstractA concise lemma is given for the construction of a semi – analytic Hamiltonian second order secular J–S planetary theory using the Jacobi – Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.

Solution of canonical equations which result from elimination of short-periodic terms in second-order planetary theory

1982 ◽  
Vol 26 (2) ◽  
pp. 143-169
Author(s):  
Jean Meffroy
Keyword(s):  
Second Order ◽  
Planetary Theory

Second order secular planetary theory for the four major planets

1984 ◽  
Vol 31 (2) ◽  
pp. 123-134 ◽  
Author(s):  
Osman M. Kamel ◽  
Abdel Aziz Bakry
Keyword(s):  
Second Order ◽  
Planetary Theory

A second order Jupiter-Saturn planetary theory

1983 ◽  
Vol 28 (2) ◽  
pp. 113-123 ◽  
Author(s):  
Osman M. Kamel ◽  
Abdel Aziz Bakry
Keyword(s):  
Second Order ◽  
Planetary Theory

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

Subsystems of Second Order Arithmetic

2009 ◽  
Author(s):  
Stephen G. Simpson
Keyword(s):  
Second Order ◽  
Second Order Arithmetic ◽  
Order Arithmetic
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