On one new modification of Alekseevskii-Tate model for nonstationary penetration of long rods into targets

New ballistics equations for long rods penetrating both elastic-plastic and brittle materials are proposed which generalize the well-known Alekseevskii-Tate equations. These equations are derived from the basis of the Lagrange-Cauchy integral for equations of nonstationary irrotational motion of ideal fluids, as well as the equations of the dynamics of expansion of a spherical cavity. Their solutions determine both the translational movement of the penetrator and the dynamics of cavity formation in the target. The structure of the equations is sufficiently simple for analysis and solution. The calculations demonstrate good qualitative agreement of the theoretical predictions with the experimental data.