Malkus水轮混沌旋转的力学机理分析

Mechanical Mechanism Analysis of Chaotic Rotation of Malkus Water Wheel

Malkus混沌水轮是展示混沌现象的典型力学装置,本文探讨了Malkus水轮混沌旋转的力学机理。把Malkus水轮混沌旋转的数学模型转换为Kolmogorov系统,基于惯性力矩、内力矩、耗散力矩和外力矩的不同耦合模式,利用理论分析和数值仿真相结合的方法,分析探讨了Malkus水轮混沌旋转的主要影响因素和内在的力学机理。影响混沌旋转现象主要因素有内能、动能和哈密顿能量。通过分析仿真得知力矩缺失模式并不能产生混沌旋转现象,全力矩模式才能产生混沌旋转现象,四种力矩缺一不可,与此同时只有耗散和外力相匹配时才能产生混沌。

Malkus chaotic water wheel is a typical mechanical device to show chaotic phenomena. This paper discusses the mechanical mechanism of Malkus chaotic rotation. The mathematical model of Malkus wheel chaotic rotation is transformed into Kolmogorov system. Based on different coupling modes of inertia moment, internal moment, dissipative moment and external moment, the main influencing factors and internal mechanical mechanism of Malkus wheel chaotic rotation are analyzed and discussed by combining theoretical analysis with numerical simulation. The main factors affecting the chaotic rotation are internal energy, kinetic energy and Hamiltonian energy. Through the analysis and simulation, we know that the lack of torque mode cannot produce chaotic rotation phenomenon;the full torque mode can produce chaotic rotation phenomenon, and four kinds of torque are indispensable, at the same time, only when the dissipation and external force match, it can produce chaos.