Energy flow characteristics of periodical orbits of nonlinear dynamical systems
Energy flow characteristics of periodical orbits of nonlinear dynamical systems
Based on energy flow theory, it is revealed that a necessary sufficient condition for nonlinear dynamical systems (NDS) 𝐲̇ = 𝐟(𝐲, 𝑡) to have periodical orbits is that there exist a non-zero spin matrix and one closed orbit with a corresponding period T, along which the time averaged flows of generalised potential energy (GPE) and generalised kinetic energy (GKE) vanish. For autonomous systems, a necessary condition to have periodical orbits is the energy flow characteristic factors (EFCFs) must not be semi-positive or semi-negative. Three examples are given to support the above revealed characteristics.
Nonlinear dynamics, Periodical orbits, Energy flow matrices, Spin matrices, Generalised potential / kinetic energies
Xing, Jing
d4fe7ae0-2668-422a-8d89-9e66527835ce
Xing, Jing
d4fe7ae0-2668-422a-8d89-9e66527835ce
Xing, Jing
(2022)
Energy flow characteristics of periodical orbits of nonlinear dynamical systems.
6 pp
.
(In Press)
Record type:
Conference or Workshop Item
(Paper)
Abstract
Based on energy flow theory, it is revealed that a necessary sufficient condition for nonlinear dynamical systems (NDS) 𝐲̇ = 𝐟(𝐲, 𝑡) to have periodical orbits is that there exist a non-zero spin matrix and one closed orbit with a corresponding period T, along which the time averaged flows of generalised potential energy (GPE) and generalised kinetic energy (GKE) vanish. For autonomous systems, a necessary condition to have periodical orbits is the energy flow characteristic factors (EFCFs) must not be semi-positive or semi-negative. Three examples are given to support the above revealed characteristics.
Text
Enoc2020-376976XingJT-Full
- Accepted Manuscript
More information
Accepted/In Press date: 17 July 2022
Keywords:
Nonlinear dynamics, Periodical orbits, Energy flow matrices, Spin matrices, Generalised potential / kinetic energies
Identifiers
Local EPrints ID: 469179
URI: http://eprints.soton.ac.uk/id/eprint/469179
PURE UUID: 7272be5d-41d6-4762-b59d-8e19caf0554d
Catalogue record
Date deposited: 08 Sep 2022 17:07
Last modified: 17 Mar 2024 06:40
Export record
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics