Autors: Georgiev, Z. D., Trushev, I. M., Todorov, T. G., Uzunov, I. M.
Title: Analytical solution of the Duffing equation
Keywords: Duffing equation, Hamiltonian function, heteroclinic trajectory, Jacobi elliptic function.

Abstract: Purpose: The purpose of this paper is to find an exact analytical expression (formula) for the periodic solutions of the double-hump Duffing equation, as well as an expression for the period of these solutions. Design/Methodology/Approach: The double-hump Duffing equation is presented as a Hamiltonian system and a phase portrait of this system is found. After analytical calculations, using Hamiltonian – based technique, the periodic solutions of this system are represented by Jacobi elliptic functions sn, cn and dn. Findings: Expressions for the periodic solutions and their periods of the double-hump Duffing equation are found. An expression for the solution (in the time domain) corresponding to the heteroclinic trajectory is also found. An important element in various applications is the obtained relationship between constant Hamiltonian levels and the elliptic modulus of the elliptic functions. Originality/value: The results obtained in the paper represent a generalization and impr

References

    Issue

    COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2020, United Kingdom, Emerald Publishing Limited, ISSN 0332-1649

    Copyright Emerald Publishing Limited ISSN: 0332-1649.

    Цитирания (Citation/s):
    1. Civelek, Cem. "Observability, controllability and stability of a nonlinear RLC circuit in form of a Duffing oscillator by means of theoretical mechanical approach." Journal of ELECTRICAL ENGINEERING, VOL 73(2022), NO2, 140–145. - 2022 - в издания, индексирани в Scopus или Web of Science

    Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus и Web of Science