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math.DG2024
Generalizing Hamiltonian Mechanics with Closed Differential Forms
Nathan Duignan, Naoki Sato
Classical Hamiltonian mechanics, characterized by a single conserved Hamiltonian (energy) and symplectic geometry, `hides' other invariants into symmetries of the Hamiltonian or in…
math.DG2024
Asymmetry of MHD equilibria for generic adapted metrics
Robert Cardona, Nathan Duignan, David Perrella
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution admits a large set of ``ada…