The simplest amplitude-period formula for non-conservative oscillators
DOI:
https://doi.org/10.31181/rme200102143hKeywords:
Periodic orbit, Non-conservative oscillator, Second order ODE.Abstract
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.
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