Rankine-Hugoniot conditions obtained by using the space-time Hamilton action

TL;DR

This paper demonstrates how Hamilton's action principle in four-dimensional space-time can derive the Rankine-Hugoniot conditions, offering a versatile approach for complex media where traditional equations are nonlinear or not explicitly known.

Contribution

It introduces a variational method in space-time to derive shock conditions, extending the applicability to complex media beyond linear differential equations.

Findings

Derivation of Rankine-Hugoniot conditions using Hamilton's action

Application of variational principles to shock-wave analysis

Potential for analyzing complex media with nonlinear equations

Abstract

In the quadri-dimensional space-time, the variation of Hamilton's action is a powerful tool to study the process equations for conservative fluid media. In this framework, Hamilton's principle allows to obtain equation of motions, equation of energy but also Rankine-Hugoniot conditions. The varia-tional method may be a versatile key to obtain the shock-wave conditions for complex media when the equations of processes are not expressed by linear or quasi-linear differential equations.