Delta shock as free piston in pressureless Euler flows

We establish the equivalence of free piston and delta shock, for one-space-dimensional pressureless compressible Euler equations. The shock appearing in singular Riemann problem is exactly that may move freely forward or backward a straight tube, driven by flows on two sides it tube. This result not only helps to understand physics somewhat mysterious shocks, but also provides way reduce fluid-solid interaction problem, which consists several initial-boundary value problems coupled with moving boundaries, simpler Cauchy problem. show from three different perspectives. first one sticky particles, derives ordinary differential equation (ODE) trajectory straightforward application conservation law momentum, physically simple clear. second study equations, as boundary following Newton's law. It depends concept Radon measure solutions equations enables us calculate force given flow. last solve directly obtain ODE generalized Rankine-Hugoniot conditions. All methods lead same ODE.