Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Hamiltonian form for General Autonomous ODE Systems: Introductory Results

Version 1 : Received: 16 December 2020 / Approved: 17 December 2020 / Online: 17 December 2020 (16:27:02 CET)

How to cite: Kobus, A. Hamiltonian form for General Autonomous ODE Systems: Introductory Results. Preprints 2020, 2020120440 (doi: 10.20944/preprints202012.0440.v1). Kobus, A. Hamiltonian form for General Autonomous ODE Systems: Introductory Results. Preprints 2020, 2020120440 (doi: 10.20944/preprints202012.0440.v1).

Abstract

New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.

Subject Areas

classical dynamics; conservation laws; ordinary differential equations; phase-space geometry

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