New Approach Development for Stability Analysis of Nonlinear Time-Dependent Dynamics

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 24 September 2024 | Viewed by 1624

Special Issue Editor

Department of Mechanical and Industrial Engineering, Texas A & M University, Kingsville, TX 78363, USA
Interests: robotics; control theory; nonlinear dynamics; human-robot interaction; advanced manufacturing; synchronization
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Special Issue Information

Dear Colleagues,

Most dynamical systems in practice are nonlinear, and stability is one of the important criteria for control design and performance analysis for nonlinear dynamical systems. Currently, there are very few tools that can be used to analyze the stability and performance of nonlinear non-autonomous dynamical systems. This Special Issue will focus on new developments and new approaches for stability analysis tools geared towards nonlinear dynamics. Contributing authors are welcome to submit papers in the areas of, but not limited to, stability analysis and tools for nonlinear dynamics, control design for nonlinear dynamics, learning- and optimization-based approach design, and new tools for the modeling of complex systems. 

Dr. Bin Wei
Guest Editor

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Keywords

  • nonlinear dynamics
  • Lyapunov stability
  • control design
  • modelling
  • robotics
  • learning and optimization

Published Papers (1 paper)

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Research

12 pages, 1541 KiB  
Article
Synchronization Analysis of Christiaan Huygens’ Coupled Pendulums
by Bin Wei
Axioms 2023, 12(9), 869; https://doi.org/10.3390/axioms12090869 - 9 Sep 2023
Viewed by 1142
Abstract
This paper discovers a new finding regarding Christiaan Huygens’ coupled pendulums. The reason Christiaan Huygens’ coupled pendulums obtain synchrony is that the coupled pendulums are subject to a harmonic forcing. As the coupled pendulums swing back and forth, they generate a harmonic force, [...] Read more.
This paper discovers a new finding regarding Christiaan Huygens’ coupled pendulums. The reason Christiaan Huygens’ coupled pendulums obtain synchrony is that the coupled pendulums are subject to a harmonic forcing. As the coupled pendulums swing back and forth, they generate a harmonic force, which, in turn drives the coupled pendulums, such that the two pendulums swing in synchrony once the angular frequency of the generated harmonic forcing satisfies a certain condition. The factor that determines the angular frequency of the generated harmonic forcing is the effective length of the pendulum, as its angular frequency solely depends on the length of the pendulum that swings about a fixed point. In other words, it is the effective length of the coupled pendulum that determines whether the coupled pendulum achieves synchrony or not. The novelty of this article is that the author explains and analyzes the synchronization behaviour of Christiaan Huygens’ coupled pendulums from the frequency and harmonic-forcing perspectives. Full article
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