It is proposed to place a space station in a short period orbit about the L₄ triangular point in the earth moon system for the purpose of communication and possibly astronomical observations. Within limits of a linear analysis, an exhaustive and general approach to the dynamical problem is presented. The equations of motion for a finite sized body of arbitrary shape and internal mass distribution are derived. The phenomenon of resonance and stability are discussed. Stability boundaries for such a space station are established. Initial conditions and pointing errors are analyzed. / Master of Science