Impact on a planar body floating on the surface of a thin layer of an inviscid incompressible fluid (Q1571220)

The author considers the impact on an arbitrary planar body floating on a thin layer of an inviscid incompressible fluid. An algorithm for constructing asymptotic solution is given. The algorithm is used to derive simple formulas for two leading-order terms of the asymptotics of the energy integral, and to derive a condition of continuous impact. These formulas contain only the solution to Dirichlet problem for Poisson's equation on the two-dimensional domain occupied by the body. The behavior of the solution near the boundaries of the body is also analyzed.