scholarly journals Mechanic: The MPI/HDF code framework for dynamical astronomy

New Astronomy ◽  
2015 ◽  
Vol 34 ◽  
pp. 98-107 ◽  
Author(s):  
Mariusz Słonina ◽  
Krzysztof Goździewski ◽  
Cezary Migaszewski
Keyword(s):  
Dynamical Astronomy

scholarly journals Astronomical Units and Constants in a Relativistic Framework

1995 ◽  
Vol 10 ◽  
pp. 201-201
Author(s):  
N. Capitaine ◽  
B. Guinot
Keyword(s):  
General Relativity ◽  
Minimum Degree ◽  
Degree Of Approximation ◽  
Theoretical Background ◽  
Point Of View ◽  
Astronomical Unit ◽  
Dynamical Astronomy ◽  
Unit Of Length ◽  
Relativistic Framework ◽  
Astronomical Constants

In 1991, IAU Resolution A4 introduced General Relativity as the theoretical background for defining celestial space-time reference sytems. It is now essential that units and constants used in dynamical astronomy be defined in the same framework, at least in a manner which is compatible with the minimum degree of approximation of the metrics given in Resolution A4.This resolution states that astronomical constants and quantities should be expressed in SI units, but does not consider the use of astronomical units. We should first evaluate the usefulness of maintaining the system of astronomical units. If this system is kept, it must be defined in the spirit of Resolution A4. According to Huang T.-Y., Han C.-H., Yi Z.-H., Xu B.-X. (What is the astronomical unit of length?, to be published in Asttron. Astrophys.), the astronomical units for time and length are units for proper quantities and are therefore proper quantities. We fully concur with this point of view. Astronomical units are used to establish the system of graduation of coordinates which appear in ephemerides: the graduation units are not, properly speaking astronomical units. Astronomical constants, expressed in SI or astronomical units, are also proper quantities.

scholarly journals Parallel/Vector Integration Methods for Dynamical Astronomy

1999 ◽  
Vol 172 ◽  
pp. 231-241
Author(s):  
Toshio Fukushima
Keyword(s):  
Large Scale ◽  
Acceleration Factor ◽  
Picard Iteration ◽  
Vector Integration ◽  
Vector Mode ◽  
Dynamical Astronomy ◽  
Vector Processors ◽  
Processor Unit ◽  
Symmetric Multistep Methods ◽  
Scalar Mode

AbstractThis paper reviews three recent works on the numerical methods to integrate ordinary differential equations (ODE), which are specially designed for parallel, vector, and/or multi-processor-unit (PU) computers. The first is the Picard-Chebyshev method (Fukushima, 1997a). It obtains a global solution of ODE in the form of Chebyshev polynomial of large (> 1000) degree by applying the Picard iteration repeatedly. The iteration converges for smooth problems and/or perturbed dynamics. The method runs around 100-1000 times faster in the vector mode than in the scalar mode of a certain computer with vector processors (Fukushima, 1997b). The second is a parallelization of a symplectic integrator (Saha et al., 1997). It regards the implicit midpoint rules covering thousands of timesteps as large-scale nonlinear equations and solves them by the fixed-point iteration. The method is applicable to Hamiltonian systems and is expected to lead an acceleration factor of around 50 in parallel computers with more than 1000 PUs. The last is a parallelization of the extrapolation method (Ito and Fukushima, 1997). It performs trial integrations in parallel. Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3.5 by using several PUs. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators (Makino and Aarseth, 1992), (Hut et al., 1995) or the implicit symmetric multistep methods (Fukushima, 1998), (Fukushima, 1999).

scholarly journals 7. Mécanique Céleste (Celestial Mechanics)

1991 ◽  
Vol 21 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Jacques Henrard
Keyword(s):  
Celestial Mechanics ◽  
Computer Technology ◽  
Reference Frames ◽  
Inertial Coordinate System ◽  
Small Bodies ◽  
Term Evolution ◽  
Dynamical Astronomy ◽  
Virginia Beach ◽  
Study Institute

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).

scholarly journals Hyperbolic normal forms and invariant manifolds: Astronomical applications

2012 ◽  
pp. 1-12 ◽  
Author(s):  
C. Efthymiopoulos
Keyword(s):  
Normal Form ◽  
Invariant Manifolds ◽  
Continuation Method ◽  
Space Mission ◽  
Mission Design ◽  
Unstable Periodic Orbits ◽  
Space Mission Design ◽  
Dynamical Astronomy ◽  
Initial Domain ◽  
Asymptotic Orbits

In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i) space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii) the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits) rely either on the use of the so-called Poincar? - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958), and developed in the canonical framework by Giorgilli (2001). We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser?s normal form.

Reminiscences and discoveries: Harold Jeffreys from 1891 to 1940

1992 ◽  
Vol 46 (2) ◽  
pp. 301-308 ◽  
Keyword(s):  
Dynamical Astronomy ◽  
Long Life

Throughout his long life Harold found absorbing interest in all aspects of nature. Most of his published work was about geophysics and dynamical astronomy, but the sixth volume of his Collected papers 1 contains those concerned with other sciences, in particular botany. In my first section I give something of the background to this early work. He was not an adventurous traveller, but he made many visits abroad when it was not so common for scientists to travel as it is now. My second section is concerned with these visits up to 1939.1 have used his reminiscences to me and also letters and photographs in my possession. Photography was for some time a hobby, and I have over 500 quarter-plate negatives and albums with prints dating from 1914; he had given up using his camera when we married in 1940. Excellent prints from some of the plates 2 were shown in St John’s College, Cambridge, in April 1991 when Professor Walter Munk, For.Mem.R.S., gave a centenary lecture.

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