Numerical solution for shape optimization of an impactor penetrating into a semi-infinite target

The shape of the impactor with the maximum depth of penetration (DOP) for a given impact velocity is found using a numerical procedure for solving a corresponding non-classical variational problem. It is shown that the optimum shape in a general case is close to a blunt cone. The variation of the optimal shape of the impactor and the dependence of the DOP vs. the initial (impact) velocity and friction coefficient is studied. The analysis is performed also for optimal conical impactors.