退化环面上的非线性jerk方程近似周期解的同伦分析方法

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振动与冲击 ›› 2010, Vol. 29 ›› Issue (5) : 46-49,7.

论文

退化环面上的非线性jerk方程近似周期解的同伦分析方法

郑敏毅;胡辉;郭源君

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Homotopy analysis method for the approximate analytical periodic solutions of a degenerate torus of a nonlinear Jerk equation

ZHENG Min-yi;HU Hui;GUO Yuan-jun

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文章历史 +

摘要

用同伦分析法求解退化环面上的非线性Jerk方程的近似周期和近似解析周期解。所得结果表明文中得到的一阶近似周期和一阶近似解析周期解与Gottlieb用低阶谐波平衡法求解得到的结果一样。当参数和初速度较大时，一阶近似周期与精确周期的百分比误差是4.8318%，而二阶近似周期与精确周期的百分比误差小于0.2199%。与数值方法给出的“精确”周期解比较，二阶近似解析周期解比一阶近似解析周期解要精确的多。因此，同伦分析法是求解非线性Jerk方程的一种非常有效的方法。

Abstract

In this paper, Homotopy Analysis Method is applied to determine the approximate periods and the approximate analytical periodic solutions of a degenerate torus of a nonlinear Jerk equation. The results obtained reveal that the first-order approximate analytical period solution and the corresponding first-order approximate period are identical to those obtained via the first-order harmonic balance approach by Gottlieb. When the parameter and the initial velocity amplitude are large, the percentage error of the first-order approximate period in relation to the exact one is 4.8318%,and the percentage error of the second-order approximate period in relation to the exact one is lower than 0.2199%. A comparison of the first and second analytical approximate periodic solutions with the numerically exact solutions shows that the second analytical approximate periodic solution is much more accurate than the first one. Thus, Homotopy Analysis Method is very effective for nonlinear Jerk equations.

导出引用

郑敏毅;胡辉;郭源君. 退化环面上的非线性jerk方程近似周期解的同伦分析方法[J]. 振动与冲击, 2010, 29(5): 46-49,7

ZHENG Min-yi;HU Hui;GUO Yuan-jun. Homotopy analysis method for the approximate analytical periodic solutions of a degenerate torus of a nonlinear Jerk equation[J]. Journal of Vibration and Shock, 2010, 29(5): 46-49,7