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Dynamics response of systems to impact or loading may be effectively treated by direct integration. However, it is often difficult to select the time-step of integration properly, especially in the case wh ich the system is badly stiff. High Precision Direct integration based on variational principle is given (HP D-VP) for homogeneous systems and HHPD-VP method for the nonhomogeneous systems are given. This method not only takes the advantage of variational principle formula, which is m uchdoi:10.1051/matecconf/20164205002 fatcat:eet52vqwkffvbjpsipell5cafq