Averaging Theory for Non-linear Oscillators
Aritra Sinha
TL;DR
This paper explores averaging theory as a method for analyzing weakly non-linear oscillators, applying it to the Van der Pol oscillator and extending its stability criteria to all integer values.
Contribution
It introduces an extended stability criterion for Van der Pol oscillators applicable to any integer n, enhancing the theoretical understanding of non-linear oscillators.
Findings
Averaging theory effectively analyzes weakly non-linear oscillators.
Extended stability criterion for Van der Pol oscillator for all integer n.
Demonstrated application of averaging theory to specific non-linear systems.
Abstract
I have first discussed how averaging theory can be an effective tool in solving weakly non-linear oscillators. Then I have applied this technique for a Van der Pol oscillator and extended the stability criterion of a Van der Pol oscillator for any integer n(odd or even).
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Taxonomy
TopicsMechanical and Optical Resonators