Tatiana Vozmishcheva
Kalashnikov Izhevsk State Technical University
Russia
Title: From zero to infinity: the limit passage of space curvature in integrable problems of celestial mechanics
Biography
Biography: Tatiana Vozmishcheva
Abstract
What can we say about the three-dimensional space in which we are living? We draw the conclusions that it has the constant zero curvature on the base of experience and studying only surrounding space that is actually incorrect. Probably, we as the Clifford worm ascribe changes of curvature to some physical actions or to changes in our organism. Small parts of space are really similar to small hills on a surface which is flat on the average, and namely there the standard laws of geometry are not true. The property of a curvedness or deformation continuously passes from one part of space to another like a wave. Variation of space curvature just is what really occurs in the phenomenon which we call the matter motion. The connection between integrable problems of celestial mechanics, the Kepler problem and the two-center problem, in the Euclid space, in the Lobachevsky space and on a sphere is investigated. The limit passage in the two-center problem in the Lobachevsky space and on a sphere is carried out as ( is a curvature of the corresponding space). The potentials and metrics in spaces under study are written in gnomonic coordinates. It is shown that integrable problem of celestial mechanics: the Kepler problem and the two-center problem, pass one to another in spaces of constant curvature under changing two parameters: the space curvature and the distance between centers. It seems natural that integrable problems of celestial mechanics should pass each other at change of space curvature.