Extended framework of Hamilton's principle applied to Duffing oscillation
Numerical Analysis
2019-03-18 v1 Computational Engineering, Finance, and Science
Computational Physics
Abstract
The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). This formulation properly accounts for initial conditions, and it recovers all the governing differential equations as its Euler-Lagrange equation. Thus, it provides elegant structure for the development of versatile temporal finite element methods. Herein, the simplest temporal finite element method is presented by adopting linear temporal shape functions. Numerical examples are included to verify and investigate performance of non-iterative algorithm in the developed method.
Keywords
Cite
@article{arxiv.1903.06524,
title = {Extended framework of Hamilton's principle applied to Duffing oscillation},
author = {Jinkyu Kim and Hyeonseok Lee and Jinwon Shin},
journal= {arXiv preprint arXiv:1903.06524},
year = {2019}
}