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A new numerical methodology is presented for simulation of dynamic behavior of floating offshore wind turbines. Wind forces are computed in the time domain through application of blade element momentum theory using the instantaneous wind velocities, blade pitch angles, and resulting rotor speed. Equations of motion are developed and solved in Euler-space, such that no small-angle assumptions are required in the solution; vessel motions are included in wind and wave force calculations. Aero-elastic effects are quantified using the industry-standard subroutine AeroDyn, with blade pitch-angles computed by the "DISCON" subroutine, both open-source and publicly available from the National Renewable Energy Lab (NREL). Effectiveness is demonstrated through a series of examples, first a case for small-angle motion is compared with results from an industry standard simulation tool for the spar-based NREL OC3-Hywind with constant wind speed and no waves; next, the same environmental conditions are applied to a smaller spar-based floater for which standard simulation tools would not be applicable. Finally, a case is presented including irregular winds and waves.