We present a dynamical analysis of the globular cluster system associated with M87 (= NGC 4486), the cD galaxy near the dynamical center of the Virgo cluster. The analysis utilizes a new spectroscopic and photometric database which is described in a companion paper (Hanes et al. 2001). Using a sample of 278 globular clusters with measured radial velocities and metallicities, and new surface density profiles based on wide-field Washington photometry, we study the dynamics of the M87 globular cluster system both globally --- for the entire cluster sample --- and separately --- for the metal-rich and metal-poor globular cluster samples. This constitutes the largest sample of radial velocities for pure Population II tracers yet assembled for any galaxy. We discuss the implications of our findings for models for the formation of giant elliptical galaxies, globular cluster systems, and the Virgo cluster. (ABRIDGED)
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