Robert I. McLachlan
Abstract
We show that the Lie bracket of an arbitrary vector field with a Hamiltonian vector field is the sum of a Hamiltonian vector field and an energy-preserving vector field, but that not all vector fields can be so decomposed.
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We show that the Lie bracket of an arbitrary vector field with a Hamiltonian vector field is the sum of a Hamiltonian vector field and an energy-preserving vector field, but that not all vector fields can be so decomposed.
Key concepts: Set (abstract data type), Mathematics, Poisson distribution, Pure mathematics, Poisson manifold, Vector field, Mathematical analysis, Geometry