A constant of motion in 3D implies a local generalized Hamiltonian structure

DOI10.1016/S0375-9601(97)00558-6zbMath0928.37007OpenAlexW2032597381MaRDI QIDQ1363217

Benito Hernández-Bermejo, Víctor Fairén

Publication date: 19 August 1997

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0375-9601(97)00558-6

zbMATH Keywords

diffeomorphismPoisson structureconstant of motionlocal generalized Hamiltonian structure

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Hamilton's equations (70H05) Dynamics induced by flows and semiflows (37C10)

Related Items

Hamiltonian dynamical systems and geometry of surfaces in 3-D, A constant of motion in 3D implies a local generalized Hamiltonian structure, Geometrical aspects of the hamiltonization problem of dynamical systems, New global solutions of the Jacobi partial differential equations, Generalization of solutions of the Jacobi PDEs associated to time reparametrizations of Poisson systems, Characterization, global analysis and integrability of a family of Poisson structures, Simple evaluation of Casimir invariants in finite-dimensional Poisson systems, Characterization and global analysis of a family of Poisson structures, One solution of the 3D Jacobi identities allows determining an infinity of them, Simple evaluation of Casimir invariants in finite-dimensional Poisson systems, Bi-Hamiltonian structure in Frenet-Serret frame

Cites Work

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• A constant of motion in 3D implies a local generalized Hamiltonian structure
• The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system
• Discrete gradient methods for solving ODEs numerically while preserving a first integral
• Generalized Hamiltonian structures for systems in three dimensions with a rescalable constant of motion
• Solving ODEs numerically while preserving a first integral