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基于何氏频率法的阻尼杜芬方程的解

Solution to a Damped Duffing Equation Using He's Frequency Approach.

作者信息

Salas Alvaro H S, Altamirano Gilder-Cieza, Sánchez-Chero Manuel

机构信息

Universidad Nacional de Colombia, Fizmako Research Group, Bogotá, Colombia.

Universidad Nacional Autónoma de Chota, Cajamarca, Peru.

出版信息

ScientificWorldJournal. 2022 Jul 11;2022:5009722. doi: 10.1155/2022/5009722. eCollection 2022.

DOI:10.1155/2022/5009722
PMID:35859637
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9293578/
Abstract

In this paper, we generalize He's frequency approach for solving the damped Duffing equation by introducing a time varying amplitude. We also solve this equation by means of the homotopy method and the Lindstedt-Poincaré method. High accurate formulas for approximating the Jacobi elliptic function cn are formally derived using Chebyshev and Pade approximation techniques.

摘要

在本文中，我们通过引入时变振幅推广了求解阻尼杜芬方程的何氏频率法。我们还通过同伦方法和林德施泰特 - 庞加莱方法求解此方程。利用切比雪夫和帕德逼近技术形式上推导了逼近雅可比椭圆函数cn的高精度公式。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/28af/9293578/c3ef4624d569/TSWJ2022-5009722.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/28af/9293578/c3ef4624d569/TSWJ2022-5009722.001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/28af/9293578/c3ef4624d569/TSWJ2022-5009722.001.jpg

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