EQUATIONS
Print ISSN: , E-ISSN: 2944-9146 An Open Access International Journal of Mathematical and Computational Methods in Science and Engineering
Volume 4, 2024
On the Homotopy-First Integral Method for Non-conservative Oscillators
Author: Andrés García
Abstract: This paper presents a ready-to-use formula for determining the number and approximate location of periodic orbits in second-order Lienard systems. As a result of the exact closed-form derived in [16], in which an ordinary differential equation (ODE) must be solved to determine the existence and location of periodic orbits for general non-conservative oscillators, a homotopy functional is defined for Lienard-type systems. This provides a closed-form and ready-to-use polynomial formula with roots as an approximation of the periodic orbit's amplitude. In addition, some examples are analyzed, along with conclusions and future plans.
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Keywords: Periodic orbits, Homotopy method, First-integral, Series expansion
Pages: 17-23
DOI: 10.37394/232021.2024.4.3
Equations, ISSN / E-ISSN: / 2944-9146, Volume 4, 2024, Art. #3