The Euler-Maupertuis principle of least action as variational inequality

International audienceStarting from Hamilton's Principle, the current paper discusses how we can derive the Euler-Maupertuis Principle of Least Action in the context of non-smooth dynamics. This variational principle allows us to directly obtain the space curve $y(x)$ of a point-mass in a potential field $V (x, y)$ without referring to the temporal dynamics. This paper generalises the Euler-Maupertuis Principle of Least Action to systems with impact by formulating the principle as a variational inequality