BOTH THE MILKY WAY (MW) AND ITS MASSIVE NEIGHBOR M31 HOST SYSTEMS OF SATELLITE DWARF GALAXIES THAT ARE RELICS OF THEIR ASSEMBLY HISTORY. NASA OBSERVATORIES SUCH AS HST WFIRST AND JWST AND SURVEY MISSIONS SUCH AS GAIA AND LSST HAVE/WILL BE USED TO IDENTIFY NEW SUBSTRUCTURE ABOUT THE MW AND M31 AND MEASURE THE KINEMATICS OF LOCAL GROUP MEMBERS WITH UNPRECEDENTED ACCURACY. THE ULTIMATE GOAL FOR THESE DATA IS TO LEARN ABOUT THE ASSEMBLY AND STRUCTURE OF THE DARK MATTER HALOS OF THE MW AND M31. TO THIS END THIS SUBSTRUCTURE (E.G. SATELLITE GALAXIES) IS TYPICALLY CONSIDERED AS ISOLATED POINT MASS-TRACERS OF THEIR HOST POTENTIALS. THIS ASSUMPTION HOWEVER BREAKS DOWN IF THE TOTAL MASS OF THE SATELLITE IS A SIGNIFICANT FRACTION OF THE HOST MASS WHICH IS THE CASE FOR THE LMC AND M33. SUCH MASSIVE SATELLITES WILL MODIFY AND CONTRIBUTE TO THE DARK MATTER DISTRIBUTION OF THE HOST CHANGING THE SHAPE OF THE HALO POTENTIAL IN A NON-SYMMETRICAL TIME-EVOLVING MANNER. AS SUCH THE LMC AND M33 HAVE THE POTENTIAL TO PERTURB THE KINEMATICS OF ALL TRACERS OF THE HALO POTENTIAL OF BOTH M31 AND THE MW SUCH AS GLOBULAR CLUSTERS HALO STARS STELLAR STREAMS AND SMALLER SATELLITES ORBITING IN THE HALO. TO DATE THIS EFFECT HAS NOT BEEN ACCOUNTED FOR IN MODELS OF THE LOCAL GROUP. THE GOAL OF THIS NASA ATP PROGRAM IS TO USE HIGH-RESOLUTION N-BODY SIMULATIONS TO BUILD TIME-EVOLVING MODELS OF THE DARK MATTER DISTRIBUTION ABOUT THE MW AND M31 OWING TO THE EVOLUTION OF THEIR MASSIVE SATELLITES. ANALYTIC REALIZATIONS OF THE RESULTING POTENTIALS WILL BE RELEASED TO THE COMMUNITY. IN ADDITION THIS PROGRAM WILL PLACE THESE NEW MODELS OF THE LOCAL GROUP AND THE EVOLUTION OF MASSIVE SATELLITES IN A COSMOLOGICAL CONTEXT. ASTROPHYSICISTS DO NOT CURRENTLY HAVE AN APPROPRIATE THEORETICAL FRAMEWORK TO STUDY THE ASSEMBLY HISTORY OF OUR LOCAL GROUP. THE PROPOSED DETAILED THEORETICAL STUDY OF HOW MASSIVE DWARFS INFLUENCE THE DARK MATTER HALO OF THEIR HOSTS IS THUS BOTH TIMELY AND CRITICAL TO ALL EFFORTS TO UNDERSTAND THE STRUCTURE AND EVOLUTION OF THE DARK MATTER DISTRIBUTION OF THE MW M31 AND ANALOGOUS SYSTEMS.