摘要
多时滞分数阶动力学系统蕴含丰富的动力学行为,研究其守恒量能更好地理解动力学行为的本质属性.基于联合Riemann-Liouville分数阶导数模型,本文建立了多时滞分数阶Pfaff-Birkhoff原理,并推导出多时滞分数阶Birkhoff系统的运动微分方程及其他形式.通过对多时滞分数阶Birkhoff系统的作用量进行变分,得到了该系统的Noether定理.最后,给出算例以说明结果的应用.
Fractional-order dynamical systems with multiple delays exhibit rich dynamic behaviors.Investigating their conserved quantities can lead to a deeper understanding of the intrinsic properties of these behaviors.Based on the combined Riemann-Liouville fractional derivative model,this paper establishes the multi-delay fractional Pfaff-Birkhoff principle and derives the differential equations of motion(along with other formulations)for multi-delay fractional Birkhoffian systems.By applying the variational principle to the action of multi-delay fractional Birkhoffian systems,we derive the Noether theorem for such systems.Finally,illustrative examples are provided to demonstrate the application of the results.
作者
杜辛雨
翟相华
DU Xinyu;ZHAI Xianghua(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China)
出处
《力学季刊》
北大核心
2025年第2期400-416,共17页
Chinese Quarterly of Mechanics
基金
国家自然科学基金(12472002,12002228)。
