  Three-body effects greatly complicate stellar evolution. We model the effects
of encounters of binaries with single stars, based on parameters chosen from
conditions prevalent in the cores of globular clusters. For our three-body
encounters, we start with a population of primordial binaries, and choose
incoming stars from the evolving single star populations of Portgies Zwart, Hut
and Verbunt (1997). In addition, we study the formation of new binaries through
tidal capture among the single stars. In subsequent papers in this series, we
will combine stellar evolution with the dynamics of a full N-body system.
