Dynamical Evolution of Self-Gravitating Systems

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Orbit-averaged Fokker-Planck equations are the fundamental evolution equation for collisional stellar dynamics. However, it is difficult to integrate the orbit-averaged Fokker-Planck equations when the number of the independent variables is equal or larger than two. Therefor, it is desirable to obtain approximate solutions. Variational Principles are useful to get such solutions. Since the orbit-averaged Fokker-Planck equations are nonlinear and non-self-adjoining, ordinary variational principles are out of use. We used the local potential proposed by Glansdorf and Prigogine and derived a variational principle.In Itoh et al. (1988) we studied the gravitational clustering of galaxies when the initial distribution of galaxies is Poisson distribution. In this period of the research, we investigated the case when the initial distribution of galaxies has power laws. We find that b appearing in f(V) depend on the volume of the sample, V. The relation between b(V) and the two-particle correlation function is obtained analytically and the results of the simulations are in agreement with it.We further investigated the effects of different mass components. For simplicity we adopted two component model where the mass of the less massive galaxy is m_1 and that of the massive galaxy is m_2. We find that f(N) derived by Saslaw and Hamilton (1984) is reproduced when m_2/m_1 < 10.