Andrés García, "On the Homotopy-First Integral Method for Non-conservative Oscillators," Equations, vol. 4, pp. 17-23, 2024, DOI:10.37394/232021.2024.4.3
Andrés García. On the Homotopy-First Integral Method for Non-conservative Oscillators.
Equations. 2024;4:17-23. 10.37394/232021.2024.4.3
EQUATIONS
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:
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.
Pages: 17-23 DOI: 10.37394/232021.2024.4.3WSEAS Transactions on Equations, E-ISSN: 2944-9146, Volume 4, 2024, Art. #3
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