A new amplitude-frequency formula for non-conservative oscillators
Andr\'es Garc\'ia
TL;DR
This paper introduces a novel amplitude-frequency formula for non-conservative oscillators, providing a new method to identify periodic orbits in complex dynamical systems.
Contribution
It formalizes the existence proof of first-integrals for second order ODEs, enabling the discrimination of periodic orbits in general non-conservative systems.
Findings
Provides a new amplitude-frequency relation for non-conservative oscillators
Establishes a formal proof of first-integrals for second order ODEs
Offers a general tool for detecting periodic orbits in complex systems
Abstract
This paper formalize the existence's proof of first-integrals for any second order ODE, allowing to discriminate periodic orbits. Up to the author's knowledge, such a powerful result is not available in the literature providing a tool to determine periodic orbits/limit cycles in the most general scenario.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Quantum chaos and dynamical systems · Microwave and Dielectric Measurement Techniques