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, within their central bulges. Some of what is found can be analogously applied to gravitational interactions of whole galaxies, e.g., in a galaxy cluster.
The overall dynamics depends highly on two factors: the density of the stars, and any overall patterns in their movement. When the density is sufficient, the group of stars is termed collisional, or when it is less, it is termed noncollisional. Patterns of movement generally fall in two classes, one being stars all orbiting around the same general circular region, examples being a disk galaxy such as a spiral galaxy. The other pattern is a group stars where the movements are not so-aligned, such as in elliptical galaxies, stellar clusters, and the central regions of spiral galaxies.
Collisional does not refer to actual star collisions (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 adjustment 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 more realistic cases (e.g., globular clusters of a million stars) draw on all these, and/or attempt to incorporate Monte Carlo methods in an effective manner.