Hamiltonian form for general autonomous ODE systems: Low dimensional examples

2020/08/27 by Kobus, Artur
#34A34 #37N05 #53Z05 #70H33 #Classical Physics (physics.class-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2008.12176

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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