1993/11/21 by Peter Névir, Richard Blender · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Analytical dynamics #Analytical mechanics #Black Holes and Theoretical Physics #Casimir effect #Classical mechanics #Compressibility #Covariant Hamiltonian field theory #Enstrophy #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Helicity #Mathematical physics #Mathematics #Mechanics #Nonlinear Waves and Solitons #Phase space #Physics #Poisson bracket #Quantum mechanics #Quantum statistical mechanics #Vortex #Vorticity
paper · doi:10.1088/0305-4470/26/22/010
openalex publication_date 1993/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Nambu mechanics generalizes discrete classical Hamiltonian dynamics. Using the Euler equations for a rotating rigid body, the connection between this representation and noncanonical Hamiltonian mechanics is shown. Nambu mechanics is extended to incompressible ideal hydrodynamical fields using energy and helicity in 3D (enstrophy in 2D). The Hamiltonian and the Casimir invariants of the non-canonical Hamiltonian theory determine the dynamics in a non-singular trilinear bracket.