Book description
TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS
Xiaoting Rui, Guoping Wang and Jianshu Zhang  Nanjing University of Science and Technology, China
Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time. First developed by the lead author and his research team, this method has found numerous engineering and technological applications. Readers are first introduced to fundamental concepts like the body dynamics equation, augmented operator and augmented eigenvector before going in depth into precision analysis and computations of eigenvalue problems as well as dynamic responses. The book also covers a combination of mixed methods and practical applications in multiple rocket launch systems, selfpropelled artillery as well as launch dynamics of onship weaponry.
• Comprehensively introduces a new method of analyzing multibody dynamics for engineers
• Provides a logical development of the transfer matrix method as applied to the dynamics of multibody systems that consist of interconnected bodies
• Features varied applications in weaponry, aeronautics, astronautics, vehicles and robotics
Written by an internationally renowned author and research team with many years' experience in multibody systems Transfer Matrix Method of Multibody System and Its Applications is an advanced level text for researchers and engineers in mechanical system dynamics. It is a comprehensive reference for advanced students and researchers in the related fields of aerospace, vehicle, robotics and weaponry engineering.
Table of contents
 Cover
 Introduction
 Foreword One for the Chinese Edition
 Foreword Two for the Chinese Edition
 Foreword Three for the Chinese Edition
 Foreword Four for the Chinese Edition
 Preface

1 Introduction
 1.1 The Status of the Multibody System Dynamics Method
 1.2 The Transfer Matrix Method and the Finite Element Method
 1.3 The Status of the Transfer Matrix Method for a Multibody System
 1.4 Features of the Transfer Matrix Method for Multibody Systems
 1.5 Launch Dynamics
 1.6 Features of this Book
 1.7 Sign Conventions

Part I: Transfer Matrix Method for Linear Multibody Systems

2 Transfer Matrix Method for Linear Multibody Systems
 2.1 Introduction
 2.2 State Vector, Transfer Equation and Transfer Matrix
 2.3 Overall Transfer Equation, Overall Transfer Matrix and Boundary Conditions
 2.4 Characteristic Equation
 2.5 Computation for State Vector and Vibration Characteristics
 2.6 Vibration Characteristics of Multibody Systems
 2.7 Eigenvalues of Damped Vibration
 2.8 Steady‐state Response to Forced Vibration
 2.9 Steady‐state Response of Forced Damped Vibration

3 Augmented Eigenvector and System Response
 3.1 Introduction
 3.2 Body Dynamics Equation and Parameter Matrices
 3.3 Basic Theory of the Orthogonality of Eigenvectors
 3.4 Augmented Eigenvectors and their Orthogonality
 3.5 Examples of the Orthogonality of Augmented Eigenvectors
 3.6 Transient Response of a Multibody System
 3.7 Steady‐state Response of a Damped Multibody System
 3.8 Steady‐state Response of a Multibody System
 3.9 Static Response of a Multibody System

4 Transfer Matrix Method for Nonlinear and Multidimensional Multibody Systems
 4.1 Introduction
 4.2 Incremental Transfer Matrix Method for Nonlinear Systems
 4.3 Finite Element Transfer Matrix Method for Two‐dimensional Systems
 4.4 Finite Element Riccati Transfer Matrix Method for Two‐dimensional Nonlinear Systems
 4.5 Fourier Series Transfer Matrix Method for Two‐dimensional Systems
 4.6 Finite Difference Transfer Matrix Method for Two‐dimensional Systems
 4.7 Transfer Matrix Method for Two‐dimensional Systems

2 Transfer Matrix Method for Linear Multibody Systems

Part II: Transfer Matrix Method for Multibody Systems

5 Transfer Matrix Method for Multi‐rigid‐body Systems
 5.1 Introduction
 5.2 State Vectors, Transfer Equations and Transfer Matrices
 5.3 Overall Transfer Equation and Overall Transfer Matrix
 5.4 Transfer Matrix of a Planar Rigid Body
 5.5 Transfer Matrix of a Spatial Rigid Body
 5.6 Transfer Matrix of a Planar Hinge
 5.7 Transfer Matrix of a Spatial Hinge
 5.8 Transfer Matrix of an Acceleration Hinge
 5.9 Algorithm of the Transfer Matrix Method for Multibody Systems
 5.10 Numerical Examples of Multibody System Dynamics
 6 Transfer Matrix Method for Multi‐flexible‐body Systems

5 Transfer Matrix Method for Multi‐rigid‐body Systems

Part III: Discrete Time Transfer Matrix Method for Multibody Systems

7 Discrete Time Transfer Matrix Method for Multibody Systems
 7.1 Introduction
 7.2 State Vector, Transfer Equation and Transfer Matrix
 7.3 Step‐by‐step Time Integration Method and Linearization
 7.4 Transfer Matrix of a Planar Rigid Body
 7.5 Transfer Matrices of Spatial Rigid Bodies
 7.6 Transfer Matrices of Planar Hinges
 7.7 Transfer Matrices of Spatial Hinges
 7.8 Algorithm of the Discrete Time Transfer Matrix Method for Multibody Systems
 7.9 Numerical Examples of Multibody System Dynamics

8 Discrete Time Transfer Matrix Method for Multi‐flexible‐body Systems
 8.1 Introduction
 8.2 Dynamics of a Flexible Body with Large Motion
 8.3 State Vector, Transfer Equation and Transfer Matrix
 8.4 Transfer Matrix of a Beam with Large Planar Motion
 8.5 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Planar Motion
 8.6 Transfer Matrices of Spring Hinges Connected to a Beam with Large Planar Motion
 8.7 Transfer Matrix of a Fixed Hinge Connected to a Beam
 8.8 Dynamics Equation of a Spatial Large Motion Beam
 8.9 Transfer Matrix of a Spatial Large Motion Beam
 8.10 Transfer Matrices of Fixed Hinges Connected to a Beam with Large Spatial Motion
 8.11 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Spatial Motion
 8.12 Transfer Matrices of Spring Hinges Connected to a Beam with Large Spatial Motion
 8.13 Algorithm of the Discrete Time Transfer Matrix Method for Multi‐flexible‐body Systems
 8.14 Planar Multi‐flexible‐body System Dynamics
 8.15 Spatial Multi‐flexible‐body System Dynamics

9 Transfer Matrix Method for Controlled Multibody Systems
 9.1 Introduction
 9.2 Mixed Transfer Matrix Method for Multibody Systems
 9.3 Finite Element Transfer Matrix Method for Multibody Systems
 9.4 Finite Segment Transfer Matrix Method for Multibody Systems
 9.5 Transfer Matrix Method for Controlled Multibody Systems I
 9.6 Transfer Matrix Method for Controlled Multibody Systems II

10 Derivation and Computation of Transfer Matrices
 10.1 Introduction
 10.2 Derivation from Dynamics Equations
 10.3 Derivation from an nth‐order Differential Equationth‐order Differential Equation
 10.4 Derivation from n First‐order Differential Equations First‐order Differential Equations
 10.5 Derivation from Stiffness Matrices
 10.6 Computational Method of the Transfer Matrix
 10.7 Improved Algorithm for Eigenvalue Problems
 10.8 Properties of the Inverse Matrix of a Transfer Matrix
 10.9 Riccati Transfer Matrix Method for Multibody Systems
 10.10 Stability of the Transfer Matrix Method for Multibody Systems

11 Theorem to Deduce the Overall Transfer Equation Automatically
 11.1 Introduction
 11.2 Topology Figure of Multibody Systems
 11.3 Automatic Deduction of the Overall Transfer Equation of a Closed‐loop System
 11.4 Automatic Deduction of the Overall Transfer Equation of a Tree System
 11.5 Automatic Deduction of the Overall Transfer Equation of a General System
 11.6 Automatic Deduction Theorem of the Overall Transfer Equation
 11.7 Numerical Example of Closed‐loop System Dynamics
 11.8 Numerical Example of Tree System Dynamics
 11.9 Numerical Example of Multi‐level System Dynamics
 11.10 Numerical Example of General System Dynamics

7 Discrete Time Transfer Matrix Method for Multibody Systems

Part IV: Applications of the Transfer Matrix Method for Multibody Systems

12 Dynamics of Multiple Launch Rocket Systems
 12.1 Introduction
 12.2 Launch Dynamics Model of the System and its Topology
 12.3 State Vector, Transfer Equation and Transfer Matrix
 12.4 Overall Transfer Equation of the System
 12.5 Vibration Characteristics of the System
 12.6 Dynamics Response of the System
 12.7 Launch Dynamics Equation and Forces Acting on the System
 12.8 Dynamics Simulation of the System and its Test Verifying
 12.9 Low Rocket Consumption Technique for the System Test
 12.10 High Launch Precision Technique for the System

13 Dynamics of Self‐propelled Launch Systems
 13.1 Introduction
 13.2 Dynamics Model of the System and its Topology
 13.3 State Vector, Transfer Equation and Transfer Matrix
 13.4 Overall Transfer Equation of the System
 13.5 Vibration Characteristics of the System
 13.6 Dynamic Response of the System
 13.7 Launch Dynamic Equations and Forces Analysis
 13.8 Dynamics Simulation of the System and its Test Verifying

14 Dynamics of Shipboard Launch Systems
 14.1 Introduction
 14.2 Dynamics Model of Shipboard Launch Systems
 14.3 State Vector, Transfer Equation and Transfer Matrix
 14.4 Overall Transfer Equation of the System
 14.5 Launch Dynamics Equation and Forces of the System
 14.6 Solution of Shipboard Launch System Motion
 14.7 Dynamics Simulation of the System and its Test Verifying

15 Transfer Matrix Library for Multibody Systems
 15.1 Introdution
 15.2 Springs
 15.3 Rotary Springs
 15.4 Elastic Hinges
 15.5 Lumped Mass Vibrating in a Longitudinal Direction
 15.6 Vibration of Rigid Bodies
 15.7 Beam with Transverse Vibration
 15.8 Shaft with Torsional Vibration
 15.9 Rod with Longitudinal Vibration
 15.10 Euler–Bernoulli Beam
 15.11 Rectangular Plate
 15.12 Disk
 15.13 Strip Element of a Two‐dimensional Thin Plate
 15.14 Thick‐walled Cylinder
 15.15 Thin‐walled Cylinder
 15.16 Coordinate Transformation Matrix
 15.17 Linearization and State Vectors
 15.18 Spring and Damper Hinges Connected to Rigid Bodies
 15.19 Smooth Hinges Connected to Rigid Bodies
 15.20 Rigid Bodies Moving in a Plane
 15.21 Spatial Rigid Bodies with Large Motion and Various Connections
 15.22 Planar Beam with Large Motion
 15.23 Spatial Beam with Large Motion
 15.24 Fixed Hinges Connected to a Planar Beam with Large Motion
 15.25 Fixed Hinges Connected to a Spatial Beam with Large Motion
 15.26 Smooth Hinges Connected to a Beam with Large Planar Motion
 15.27 Smooth Hinges Connected to a Beam with Large Spatial Motion
 15.28 Elastic Hinges Connected to a Beam with Large Planar Motion
 15.29 Elastic Hinges Connected to a Beam Moving in Space
 15.30 Controlled Elements of a Linear System
 15.31 Controlled Elements of a General Time‐variable System

12 Dynamics of Multiple Launch Rocket Systems
 Appendix I: Rotation Formula Around an Axis
 Appendix II: Orientation of a Body‐fixed Coordinate System
 Appendix III: List of Symbols
 Appendix IV: International Academic Communion for the Transfer Matrix Method for Multibody Systems
 References
 Index
 End User License Agreement
Product information
 Title: Transfer Matrix Method for Multibody Systems
 Author(s):
 Release date: November 2018
 Publisher(s): Wiley
 ISBN: 9781118724804
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