Hamiltonian form for general autonomous ODE systems: Low dimensional examples

Artur Kobus

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arXiv · 2008.12176

Hamiltonian form for general autonomous ODE systems: Low dimensional examples

Artur Kobus

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Abstract

Paper is devoted to maintaining the simple objective: We want to provide Hamiltonian canonical form for autonomous dynamical system reducible to even-dimensional one. Along the road we construct new class of conserved quantities, called effectively conserved, that have dissimilar properties to traditional first integrals (e.g. differential of effectively conserved quantity being a Pfaffian form). We do not confine the discussion to physics; we consider examples from biology and chemistry, giving direct recipe for how to engage the framework in occurring problems. Perspective for future application in geometric numerical methods is given.

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Artur Kobus. 2020-08-27. Hamiltonian form for general autonomous ODE systems: Low dimensional examples. https://arxiv.org/abs/2008.12176

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