Periodic Motions to Chaos in a Spring-Pendulum System / by Yu Guo, Albert C. J. Luo.

Format:

Book

Author/Creator:

Guo, Yu, Author.

Luo, Albert C. J., Author.

Contributor:

SpringerLink (Online service)

Series:

Synthesis lectures on mechanical engineering 2573-3176

Synthesis Lectures on Mechanical Engineering, 2573-3176

Language:

English

Subjects (All):

Mechanical engineering.

Engineering mathematics.

Engineering-Data processing.

Plasma waves.

Mechanical Engineering.

Mathematical and Computational Engineering Applications.

Waves, instabilities and nonlinear plasma dynamics.

Local Subjects:

Mechanical Engineering.

Mathematical and Computational Engineering Applications.

Waves, instabilities and nonlinear plasma dynamics.

Physical Description:

1 online resource (XI, 104 pages 63 illustrations, 58 illustrations in color)

Edition:

1st ed. 2023.

Contained In:

Springer Nature eBook

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2023.

System Details:

text file PDF

Summary:

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.

Contents:

Preface

Introduction

Chapter 1 - A Semi-Analytical Method

Chapter 2 - Discretization of a Spring-Pendulum

Chapter 3 - Formulation for Periodic motions

Chapter 4 - Period 1 motions to chaos varying with harmonic frequency

Chapter 5 - Period 1 motions to chaos varying with harmonic amplitude

Chapter 6 - Higher-order periodic motions to chaos

References.

Other Format:

Printed edition:

ISBN:

9783031178832

Access Restriction:

Restricted for use by site license.