一类时变非线性系统的精确解
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国家自然科学基金资助项目(12472001)和江苏大学高级人才启动基金(21JDG057)

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    摘要:

    本文提出了一种新的时空非线性变换,并将其应用于一类时变非线性系统的求解问题.通过坐标变换推导了系统的可积条件,得到可解的常系数线性微分方程.基于逆变换和常系数线性微分方程的解析解,导出了原系统的精确解.把1/2阶贝塞尔方程作为该类时变非线性系统的特殊情况,并利用该理论得到其精确解.最后,通过一些数值仿真验证了该方法的有效性和正确性.

    Abstract:

    In this paper, a new space-time nonlinear transformation is proposed and applied to a class of time-varying nonlinear systems. Then the integrability condition of the system is derived by coordinate transformation, and the linear differential equation with constant coefficients is obtained. Based on the inverse nonlinear transformation and the analytic solution of linear differential equations with constant coefficients, the exact solution of the original system is derived. The 1/2 order Bessel equation is taken as a special case of this kind of time-varying nonlinear system, and its exact solution is obtained by using this theory. Finally, the effectiveness and correctness of the proposed method are verified by some numerical simulations.

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刘畅,王国夫,宋禹含,姜文安.一类时变非线性系统的精确解[J].动力学与控制学报,2025,23(3):56~64; Liu Chang, Wang Guofu, Song Yuhan, Jiang Wenan. Exact Solution for A Class of Time-Varying Nonlinear Systems[J]. Journal of Dynamics and Control,2025,23(3):56-64.

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历史
  • 收稿日期:2024-11-28
  • 最后修改日期:2025-01-21
  • 在线发布日期: 2025-03-25
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