TITLE:
Modification of the Lagrange-Jacobi Equation and Its Application
AUTHORS:
Chingis Omarov, Gulnara Omarova
KEYWORDS:
Celestial Mechanics, Large-Scale Structure of Universe, Galaxies, Clusters, Cosmological Epoch
JOURNAL NAME:
World Journal of Mechanics,
Vol.13 No.6,
June
30,
2023
ABSTRACT: The Lagrange-Jacobi equation is one of the significant tools for
the qualitative analysis of the n-body problem. In this paper, we
present the modified Lagrange-Jacobi equation by introducing a
new formal parameter of n-body problem and propose its application to the dynamical
study of clusters of galaxies which are large-scale structures of Universe. We put forward
and study a new dynamical problem which is related to the stage of relaxation
of observed stationary clusters of galaxies which are considered as a non-equilibrium
systems of point masses. We also received the analytical form of the potential
energy of such galaxy clusters. One of the applications of this analytical form
is the analytical relation between the time of setting up the virial
equilibrium in relaxing clusters of galaxies and the cosmological epoch T.