We formulate the principle of nonconservative stationary action introduced by Galley[Gal13, GTS14] in a geometrical manner, generalising it to the setting on a Rieman-nian manifold. The principle relies on an action of the doubled variables which yieldscoupled equations of motion. The subset of the solutions to the coupled equationswhere both paths coincide is interpreted as the physical motion. As a case study weshow how the Navier–Stokes equations can be obtained from an action functionalinvolving a viscous coupling term of the two variables. We study assumptions underwhich solutions of the coupled system are on the physical submanifold. We high-light that in general transforming the doubled action between reference frames is notpossible and caution should be taken when using mean and difference variables as in[GTS14]. Furthermore we formulate a version of Noether’s theorem which can beapplied to systems with applied forces to obtain balance laws from symmetries of aconservative subsystem.
A geometric view on Galley's nonconservative action principle
Kowalewski, R. (Author). 18 Feb 2026
Student thesis: Doctoral Thesis › PhD