Open AccessThe simplest amplitude-period formula for non-conservative oscillators
Author(s) -
JiHuan He,
Andrés García
Publication year - 2021
Publication title -
reports in mechanical engineering
Language(s) - English
Resource type - Journals
ISSN - 2683-5894
DOI - 10.31181/rme200102143h
Subject(s) - periodic orbits , amplitude , limit (mathematics) , period (music) , ordinary differential equation , mathematics , mathematical analysis , differential equation , work (physics) , periodic function , physics , classical mechanics , quantum mechanics , acoustics
The simplest frequency formulation for conservative oscillators was proposed in 2019 (Results Phys 2019;15:102546). However, it becomes invalid for non-conservative oscillators. This work suggests the simplest amplitude-period formulation for non-conservative oscillators. The existence of a periodic solution of a second-order ordinary differential equation is given, and the periodic orbits are easily obtained. To the best of the authors’ knowledge, such a powerful result is not available in the literature, providing a tool to determining periodic orbits/limit cycles in the most general scenario.