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Stellar dynamics is the study of the forces between and motions of stars within a group that are close enough to each other that their gravity affects their neighbors. Groups of interest are galaxies, globular clusters, open clusters, and the central regions of galaxies that have a density of stars similar to such stellar clusters (e.g., a stellar nucleus), generally within their central bulges. Some of what is found regarding so many objects interacting gravitationally can be analogously applied to gravitational interactions between whole galaxies, e.g., in a galaxy cluster.
The overall dynamics largely depends on two characteristics: the density of the stars, and any existing overall pattern in their movement. A group of stars is termed collisional if above a certain density, and if not, it is termed noncollisional. Patterns of movement fall into two general classes, one being stars all orbiting around the same general circular region comprising a disk, examples being a disk galaxy such as a spiral galaxy. The other general pattern is a group stars where the movements are not so-aligned, i.e., more random, such as in elliptical galaxies, stellar clusters, and the central regions of spiral galaxies.
Collisional does not imply actual star impacts (though this does occasionally happen), but that there are encounters sufficiently close that their effect is similar to that between objects bouncing or repelling, as are molecules in a gas. Such a stellar encounter is called a strong encounter (strong gravitational encounter), i.e., stars that approach so close that their change in velocity is in the same order-of-magnitude as their original velocity, as opposed to weak encounters or weak gravitational encounters, where the result is just a small change to the star's velocity.
One means of studying stellar dynamics is N-body simulations, a method limited by the number of stars that can practically be simulated on today's computers, there being a trade-off between the time and other resources necessary to do a simulation versus the count of stars in the group being simulated. To investigate larger groups without the benefit of such simulations, methods are borrowed from the study of gases, treating stars like particles (e.g., molecules) and finding probability distributions regarding their characteristics and the evolution of those characteristics. Tools include the Boltzmann equation which models interacting particles (also allowing accommodation of external forces) that have not yet settled into an equilibrium (the Maxwell-Boltzmann distribution is an example of a distribution of particles that are in equilibrium), and equations that deal with special cases, such as the Fokker-Planck equation. The latter represents a limiting case given certain characteristics, sometimes termed the Fokker-Planck limit. Efforts to analyze realistic cases with large numbers of stars (e.g., globular clusters of a million stars) draw on all these, and/or attempt to incorporate Monte Carlo methods in an effective manner.