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Modeling of the global motion of mechanical systems superimposed by large flexible deflections and small deformations are subjects that require special consideration. One of the main problems in the dynamics simulation of moving systems it is the precision of the dynamics equations. Novel generalized Newton - Euler dynamic equations for rigid and flexible bodies are proposed. Unified approach to simulation of rigid and flexible systems is developed. The dynamic equations are expressed with respect to the quasi - velocities and accelerations as for the flexible nodes so for the rigid bodies....