Instabilities of motions in a combustion chamber are consequences of the coupled dynamics of
combustion processes and of the flow in the chamber. The extreme complexities of the problem
always require approximations of various sorts to make progress in understanding the
mechanisms and behavior of combustion instabilities. This paper covers recent progress in the
subject, mainly summarizing efforts in two areas: approximate analysis based on a form of
Galerkin's method, particularly useful for understanding the global linear and nonlinear
dynamics of combustion instabilities and numerical simulations intended to accommodate as
fully as possible fundamental chemical processes in both the condensed and gaseous phases.
One purpose of current work is to bring closer together these approaches to produce more
comprehensive and detailed realistic results applicable to the interpretation of observations
and for design of new rockets for both space and military applications. Particularly important
are the goals of determining the connections between chemical composition and instabilities;
and the influences of geometry on nonlinear behavior
