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In this paper, it is discussed the approximation of the nonlinear equations of motion of mechanical systems used on different operators achieved level displacements and displacement increments. For the numerical solution of the problem, we used the scheme of direct integration of the equations of motion, which in the case of a linear problem reduces to the known Newmark scheme. The stability parameter of the integration scheme is determined. Analytical calculations are confirmed on the test meeting of the model task

Stability of direct circuits integrating the equations of motion in the simulation of the dynamics of destruction