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by Jianshu Zhang, Guoping Wang, Xiaoting Rui
Transfer Matrix Method for Multibody Systems
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
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
6.1 Introduction
6.2 State Vector, Transfer Equation and Transfer Matrix
6.3 Overall Transfer Equation and Overall Transfer Matrix
6.4 Transfer Matrix of a Planar Beam
6.5 Transfer Matrix of a Spatial Beam
6.6 Numerical Examples of Multi‐flexible‐body System Dynamics
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
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
Appendix I: Rotation Formula Around an Axis
Appendix II: Orientation of a Body‐fixed Coordinate System
II.1 First Rotation
II.2 Second Rotation
II.3 Third Rotation
Appendix III: List of Symbols
Appendix IV: International Academic Communion for the Transfer Matrix Method for Multibody Systems
References
Index
End User License Agreement
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