圆锥连续型水轮混沌旋转的力学机理分析与能量演化研究  

Mechanical Mechanism Analysis and Energy Evolution Study of Chaotic Rotation of Conical Continuous Waterwheel

作　　者：王贺元 何香红 梅鹏飞 WANG Heyuan;HE Xianghong;MEI Pengfei(College of General Education,Guangdong University of Science and Technology,Dongguan 523083,China;College of Mathematics and Systematics Sciences,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]广东科技学院通识教育学院,广东东莞523083 [2]沈阳师范大学数学与系统科学学院,辽宁沈阳110034

出　　处：《应用数学》2024年第4期912-923,共12页Mathematica Applicata

基　　金：国家自然科学基金(11572146);广东科技学院科研基金(GKY-2023KYZDK-14);广东科技学院博士科研启动基金项目(GKY-2022BSQD-36)。

摘　　要：本文探讨圆锥连续型水轮混沌旋转的力学机理与能量转换问题.基于不同的力矩耦合模式下系统动力学行为的对比分析,获得了圆锥连续型水轮系统产生混沌的主要影响因素和形成机制,进而阐释了圆锥连续型水轮混沌旋转的力学机理.引入卡西米尔函数分析圆锥连续型水轮系统的动力学行为和能量之间的相互转换,估计了混沌吸引子的边界.讨论能量与Rayleigh数之间的关系.Based on the comparative analysis of the dynamic behavior of the system under di?erent torque coupling modes,This paper discusses the mainin?uencing factors and formation mechanism of chaos in conical continuous waterwheel system,and then explains the mechanical mechanism of chaotic rotation of conical continuous waterwheel.The casimir function is introduced to analyze the dynamic behavior and energy conversion of the mathematical model,and the boundary of chaotic attractor is estimated.The relationship between energy and Rayleigh number is studied.

关 键 词：圆锥连续型水轮 力学机理 KOLMOGOROV系统 混沌 

分 类 号：O175.1[理学—数学] O192[理学—基础数学] O193O302