Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy

2014 ◽  
pp. 187-226 ◽  
1991 ◽  
Vol 21 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Jacques Henrard

During 1988–1990 Commission 7 has sponsored or co-sponsored several IAU conferences: Colloquium No. 109 “Application of Computer Technology to Dynamical Astronomy” (Gaithersburg, July 1988), Symposium No. 141 “Inertial Coordinate System on the Sky” (Pulkovo, October 1989), Colloquium No. 127 “Reference Frames” (Virginia Beach, October 1990), Colloquium No. 132 “Instability, Chaos and Predictability in Celestial Mechanics and Stellar Systems” (Delhi, October 1990). The colloquium No. 118 “Dynamics of Small Bodies in the Solar System” which was to be held in Nanjing in June 1989 had unfortunately to be postponed then cancelled. Other meetings of interest to the members of Commission 7 were the 2nd Alexander von Humbolt Colloquium on “Long Term Evolution of Planetary Systems” (Ramsau, March 1988), the Colloquium “Asteroids, Comets, Meteors III” (Uppsala, June 1989), the colloquium “Mécanique Céleste et Systèmes Hamiltoniens” (Luminy, May 1990) and the NATO Advanced Study Institute on “Predictability, Stability and Chaos in N-Body Dynamical Systems” (Cortina d’Ampezzo, August 1990).


2005 ◽  
Vol 1 (T26A) ◽  
pp. 181-181
Author(s):  
Kennet P. Seidelman ◽  
M.F. A'HEARN ◽  
D.P. CRUIKSHANK ◽  
J.L. HILTON ◽  
H.U. KELLER ◽  
...  

The 2003 report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements has appeared in Celestial Mechanics and Dynamical Astronomy(2005)volume 91, part 3–4, pages 203–215. The Working Group continues to maintain and update the information for cartographic coordinates and rotational elements for the Sun, Moon, planets, satellites, asteroids, and comets. A report is published treannually. A web site is maintained at http://extranet.astrogeology.wr.usgs.gov/Projects/WGCCRE with the up-to-date information. It is anticipated that the next report will include updates for Saturn (rotation rate) and all of the Saturnian moons, additions for the newly visited comets and asteroids, and a clarification of the Moon's coordinate systems (the mean Earth/polar axis system needs to be defined more precisely).


In this paper the author proposes to investigate the true geometrical basis of that entire class of algebraical expressions, known to mathematicians as elliptic functions or integrals. He sets out by showing what had already been done in this department of the subject by preceding geometers. That the elliptic integral of the second order represented an arc of a plane ellipse, was evident from the beginning.


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