Periodic Motions to Chaos in a Spring-Pendulum System

Guo, Yu, Luo, Albert C. J.

Periodic Motions to Chaos in a Spring-Pendulum System
  • 出版商: Springer
  • 出版日期: 2024-02-07
  • 售價: $2,520
  • 貴賓價: 9.5 折 $2,394
  • 語言: 英文
  • 頁數: 104
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031178858
  • ISBN-13: 9783031178856

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商品描述

This book builds on the fundamental understandings, learned in undergraduate engineering and physics in principles of dynamics and control of mechanical systems. The design of real-world mechanical systems and devices becomes far more complex than the spring-pendulum system to which most engineers have been exposed. The authors provide one of the simplest models of nonlinear dynamical systems for learning complex nonlinear dynamical systems.

The book addresses the complex challenges of the necessary modeling for the design of machines. The book addresses the methods to create a mechanical system with stable and unstable motions in environments influenced by an array of motion complexity including varied excitation frequencies ranging from periodic motions to chaos.

Periodic motions to chaos, in a periodically forced nonlinear spring pendulum system, are presented through the discrete mapping method, and the corresponding stability and bifurcations of periodic motions on the bifurcation trees are presented. Developed semi-analytical solutions of periodical motions to chaos help the reader to understand complex nonlinear dynamical behaviors in nonlinear dynamical systems. Especially, one can use unstable motions rather than stable motions only.

商品描述(中文翻譯)

本書建立在本科工程和物理學中學習的動力學和機械系統控制的基本理解之上。現實世界中機械系統和裝置的設計變得比大多數工程師所接觸的彈簧擺系統要複雜得多。作者提供了非線性動態系統的一個最簡單模型，以便學習複雜的非線性動態系統。

本書針對設計機器所需建模的複雜挑戰進行探討。書中討論了在受多種運動複雜性影響的環境中創建具有穩定和不穩定運動的機械系統的方法，包括從週期運動到混沌的各種激勵頻率。

在一個周期性強迫的非線性彈簧擺系統中，通過離散映射方法展示了從週期運動到混沌的過程，並呈現了週期運動在分岔樹上的相應穩定性和分岔情況。發展出的周期運動到混沌的半解析解幫助讀者理解非線性動態系統中的複雜非線性動態行為。特別是，可以使用不穩定運動而不僅僅是穩定運動。

作者簡介

Dr. Yu Guo worked at Midwestern State University Texas as an Associate Professor. He previously worked at Caterpillar Inc. as an engine structural and dynamics engineer. Dr. Guo conducts research focusing on nonlinear vibration and impact dynamics. He has published 18 peer-reviewed journal papers, more than 20 conference articles, 4 book chapters, and 2 monographs. He has also conducted many professional presentations or invited lectures all over the world.

Professor Albert C.J. Luo has worked at Southern Illinois University Edwardsville. For over 30 years, Dr. Luo's contributions to nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems; (ii) dynamical systems synchronization; (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems; (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems; and (v) the full nonlinear theory for a deformablebody. Such contributions have been scattered into 28 monographs and over 350 peer-reviewed journal and conference papers. Dr. Luo served as an editor for the Journal of Communications in Nonlinear Science and Numerical Simulation, and book series on Nonlinear Physical Science (HEP and Springer) and Nonlinear Systems and Complexity (Springer). Dr. Luo was an editorial member for IMeCh E Part K Journal of Multibody Dynamics and Journal of Vibration and Control and has also organized over 30 international symposiums and conferences on dynamics and control.

作者簡介(中文翻譯)

Dr. Yu Guo 曾在德州中西部州立大學擔任副教授。他之前在卡特彼勒公司擔任引擎結構與動力學工程師。郭博士的研究專注於非線性振動和衝擊動力學。他已發表18篇經過同行評審的期刊論文、超過20篇會議文章、4章書籍章節以及2本專著。他還在全球各地進行了許多專業演講或受邀講座。

Professor Albert C.J. Luo 曾在南伊利諾伊大學愛德華茲維爾校區工作。超過30年來，羅博士對非線性動力系統和力學的貢獻包括：(i) 不連續動力系統的局部奇異性理論；(ii) 動力系統的同步；(iii) 非線性動力系統中週期和混沌運動的解析解；(iv) 非線性哈密頓系統中的隨機和共振層理論；以及 (v) 可變形體的完整非線性理論。這些貢獻已散佈於28本專著和超過350篇經過同行評審的期刊及會議論文。羅博士曾擔任《非線性科學與數值模擬通訊期刊》的編輯，以及《非線性物理科學》（HEP和Springer）和《非線性系統與複雜性》（Springer）書系的編輯。羅博士還是 IMechE Part K 多體動力學期刊和振動與控制期刊的編輯成員，並組織了超過30場國際動力學與控制的研討會和會議。

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