Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems

Li Li

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Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems

机译：强非线性非自治系统的近似周期解的能量方法

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摘要

A theorem for the periodic solution of strongly nonlinear nonautonomous systems is proved based upon the concept of the conservation of average energy. By using this theorem not only the necessary and sufficient conditions for the existence and stability of the periodic solutions and the approximate expressions for those periodic solutions can be obtained.

机译：基于平均能量守恒的概念，证明了强非线性非自治系统周期解的一个定理。通过使用该定理，不仅可以获得周期解的存在和稳定性的必要和充分条件，而且可以获得这些周期解的近似表达式。

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来源
《Nonlinear dynamics》 |1999年第3期|共24页
作者
Li Li;
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正文语种 eng
中图分类动力学;
关键词
Nonlinear systems; Theorem proving; Vibrations (mechanical); Approximation theory; Perturbation techniques; Energy method; Nonlinear nonautonomous systems;

机译：非线性系统;定理证明;振动（机械）;逼近理论;摄动技术;能量方法;非线性非自治系统;

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专利

1. Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems [J] . Li Li Nonlinear dynamics . 1999,第3期

机译：强非线性非自治系统的近似周期解的能量方法
2. Periodic Solution for Strongly Nonlinear Vibration Systems by He's Energy Balance Method [J] . Ganji SS, Ganji DD, Ganji ZZ, Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 2009,第1期

机译：He能量平衡法求解强非线性振动系统的周期解
3. Energy method for computing periodic solutions of strongly nonlinear autonomous systems with multi-degree-of-freedom [J] . Li L., Ye HL. Nonlinear dynamics . 2003,第1期

机译：具有多自由度的强非线性自治系统周期解的能量方法
4. Positive Periodic Solutions of Nonautonomous Competitive Systems with Distributed Delay and Weak Allee Effect [C] . Jizeng Wei, Wei Guo, jizhou Sun, Conference of Biomathematics . 2008

机译：具有时滞和Allee效应的非自治竞争系统的正周期解。
5. Multiple periodic solutions for nonautonomous asymptotically linear Hamiltonian systems. [D] . Wang, Chengwen. 2000

机译：非自治渐近线性哈密顿系统的多个周期解。
6. Jacobi spectral collocation method for the approximate solution of multidimensional nonlinear Volterra integral equation [O] . Yunxia Wei, Yanping Chen, Xiulian Shi, -1

机译：多维非线性Volterra积分方程近似解的Jacobi谱配点法
7. APPROXIMATE ANALYTICAL SOLUTIONS TO NONLINEAR OSCILLATIONS OF NON-NATURAL SYSTEMS USING HE’S ENERGY BALANCE METHOD [O] . D. D. Ganji, S. Karimpour, S. S. Ganji 2015

机译：用能量平衡法逼近非自然系统非线性振动的解析解
8. Approximate Solution (with Error Bounds) to a Nonlinear, Nonautonomous Second-Order Differential Equation. [R] . Taylor, J. G. 1978

机译：非线性非自治二阶微分方程的近似解（带误差界）。

Energy method for approximate periodic solution of strongly nonlinear nonautonomous systems

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