Lagrangian and Hamiltonian treatments of non-conservative systems

par M. Christopher Aykroyd (LTE, Observatoire de Paris)

jeudi 12 juin 2025, 14:00 → 16:00 Europe/Paris

Denisse (Observatoire de Paris)

We present a novel extension of Hamiltonian mechanics to non-conservative systems built upon the Schwinger-Keldysh-Galley double-variable formalism. We begin by outlining Galley's action principle for initial-value problems, and how it enables a description of non-conservative processes from a Lagrangian standpoint. We clarify important subtleties regarding boundary conditions, the emergence of the physical trajectory, and a class of gauge transformations on the canonical momenta. Next, from a Legendre transform, we construct the corresponding family of gauge-related nonconservative Hamiltonians. We show that virtually any classical initial-value problem can be embedded on this enlarged symplectic manifold, supplying the associated Hamiltonian and Lagrangian functions explicitly. As a further contribution, we derive a completely equivalent linear "Lie" formulation of the double-variable action and Hamiltonian which streamlines computations and renders transparent many structural properties of the formalism.