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 arelarge-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.
References
[1]
Duboshin, G.N. (1975) Celestial Mechanics. Basic Problems and Methods. Nauka, Moscow, 586 p.
[2]
Peebles, P.J.E. (1993) Principles of Physical Cosmology. Princeton University Press, Princeton, 718 p.
[3]
Saslaw, C. (1987) Gravitational Physics of Stellar and Galactic Systems. Cambridge University Press, Cambridge, 512 p.
[4]
Lynden-Bell, D. (1967) Statistical Mechanics of Violent Relaxation in Stellar Systems. MNRAS, 136, 101-121. https://doi.org/10.1093/mnras/136.1.101
Binney, J. and Tremaine, S. (2008) Galactic Dynamics. 2nd Edition, Princeton University Press, Princeton, 885 p. https://doi.org/10.1515/9781400828722
[7]
Sensui, T., et al. (1999) Evolution of Clusters of Galaxies: Mass Stripping from Galaxies and Growth of Common Halos. Publications of the Astronomical Society of Japan, 51, 943-954. https://doi.org/10.1093/pasj/51.6.943
