The violent and messy physics of a sonic boom can now be described using the same elegant math that predicts the orbit of a planet.
Shocks and explosions are usually treated as broken systems in physics because they create sudden, discontinuous jumps in pressure and speed. Researchers have now modified Hamilton's principle, a bedrock of physics, to account for these jagged events directly. This allows scientists to use energy conservation laws to derive exactly how a shock wave will behave without using complex workarounds. It bridges a massive gap between the smooth, predictable parts of nature and its most violent outbursts. This discovery will lead to much better designs for everything from supersonic jets to high-speed medical imaging.
Variational Principles for Shock Dynamics in Compressible Euler Flows
arXiv · 2604.20635
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is restricted to smooth solutions and does not directly accommodate shock discontinuities. Addressing this limitation within a variational framework has long been a challenging issue. In this paper, we develop a variational framework that extends Hamilton's princip