Open problems on the eve of the next millennium
type: Item
instance of: scholarly article
title: Open problems on the eve of the next millennium
zbMATH Open document ID: 0887.70012
DOI: 10.1007/BF00048447
author: Victor Szebehely
published in: Celestial Mechanics and Dynamical Astronomy
publication date: 1998-05-25T00:00:00Z
review text: This paper contains some interesting opinions of the author on some open problems in the field of celestial mechanics for the next century. It must be noticed that Prof. Szebehely is a well-known authority in this field, particularly in the restricted problem of three bodies, and consequently his opinions have a special value. The paper starts with some historical remarks on the evolution of celestial mechanics from Copernicus up to the present century. Then the author comments briefly on the open problems which pose the non-integrable systems in this field by introducing an illustrative example which shows how the reduction techniques allow to gain insight into the properties of the flow and also into the underlying field of forces. Finally, he points out that, taking into account the increasing improvements of computer technologies, it is expected that new numerical techniques will allow to have a better knowledge of many problems of celestial mechanics and, on the other hand, with the help of statistical mechanics the statistical approach will gain importance in the future.
Mathematics Subject Classification ID: 70F15
Mathematics Subject Classification ID: 70-02
zbMATH DE Number: 1051508
zbMATH Keywords: non-integrable systems
zbMATH Keywords: reduction techniques
zbMATH Keywords: computer technologies
zbMATH Keywords: numerical techniques
zbMATH Keywords: statistical mechanics
zbMATH Keywords: statistical approach
reviewed by: Manuel Calvo
MaRDI profile type: Publication
cites work: Q3844116
cites work: Q3995849
cites work: BURRAU'S PROBLEM OF THREE BODIES
full work available at URL: https://doi.org/10.1007/bf00048447
OpenAlex ID: W2068390412
description: scientific article; zbMATH DE number 1051508