The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we find interesting dynamics of the orientational moduli. A detailed study of the inter-vortex force is provided and a phase diagram separating Abelian and non-Abelian vortex types is constructed. Some results on scatterings with non-zero impact parameter and multi-vortex collisions are included.
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