Dynamic Mechanism and Energy Evolution of the Waterwheel Chaotic Rotation

WANG Heyuan; XIAO Shengzhong; MEI Pengfei; ZHANG Xi

doi:10.21656/1000-0887.420336

Volume 44 Issue 5

May 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(5): 560-572

WANG Heyuan, XIAO Shengzhong, MEI Pengfei, ZHANG Xi. Dynamic Mechanism and Energy Evolution of the Waterwheel Chaotic Rotation[J]. Applied Mathematics and Mechanics, 2023, 44(5): 560-572. doi: 10.21656/1000-0887.420336

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Dynamic Mechanism and Energy Evolution of the Waterwheel Chaotic Rotation

doi: 10.21656/1000-0887.420336

WANG Heyuan^{1, 2
,},
XIAO Shengzhong^{3
,
,},
MEI Pengfei²,
ZHANG Xi²

1.
College of General Education, Guangdong University of Science & Technology, Dongguan, Guangdong 523083, P.R.China
2.
School of Mathematics and System Science, Shenyang Normal University, Shenyang 110034, P.R.China
3.
Guangdong AIB College, Guangzhou 510507, P.R.China

Received Date: 2021-11-08
Rev Recd Date: 2022-01-13
Publish Date: 2023-05-01

Abstract

Abstract

To reveal the mechanism of the waterwheel chaotic rotation, the dynamic mechanism and the energy conversion of the waterwheel chaotic rotation were studied with the method of moment analysis. The mathematical model for the Malkus waterwheel rotation was transformed into the Kolmogorov system. Based on the different coupling modes of inertia moments, internal moments, dissipation moments and external moments, the main factors and internal dynamic mechanisms of the Malkus waterwheel chaotic rotation were analyzed and discussed with the method of theoretical analysis and numerical simulation. The conversion among the Hamiltonian energy, the kinetic energy and the potential energy was investigated. The relationship between the energies and the Rayleigh number was discussed. The main factors influencing the chaotic rotation are the external moments and the dissipation moments. The analysis and simulation results show that, the lack-of-moment mode cannot lead to the system chaos, but the full-moment mode can, i.e., the waterwheel chaotic rotation will occur only in the existence of all 4 types of moments and when the dissipation and external forces match well. The Casimir function was introduced to analyze the system dynamics and the energy conversion. The bounds for the chaotic attractor were obtained with the Casimir function. The Casimir function reflects the energy conversion and the distances between the orbits and the equilibria. Numerical simulations depict the relationships among them.
- Kolmogorov system,
- chaos,
- waterwheel system,
- dynamic mechanism

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References(22)

References

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