Multibody System Simulation,9783540656623

Multibody System Simulation

by
ISBN13: 9783540656623
ISBN10: 3540656626
Format: Paperback
Pub. Date: 1999-11-01
Publisher(s): Springer Verlag
List Price: $212.92

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Summary

The book presents innovative methods for the solution of multibody descriptor models. It emphasizes the interdependence of modeling and numerical solution of the arising system of differential-algebraic equations (DAE). Here, it is shown that modifications of non-stiff ODE-solvers are very effective for a large class of multibody systems. In particular, implicit methods are found to dovetail optimally with the linearly implicit structure of the model equations, allowing an inverse dynamics approach for their solution. Furthermore, the book stresses the importance of software development in scientific computing and thus presents a complete example of an interdisciplinary problem solution for an important field of application from technical mechanics.

Table of Contents

Introduction 1(8)
Multibody Systems in Technical Mechanics
9(52)
Multibody Systems
11(10)
Topology of MBS
12(2)
Typical Applications in Technical Mechanics
14(7)
Equations of Motion of MBS in Descriptor Form
21(6)
Types of Constraints
21(2)
Hamilton's Principle
23(2)
d'Alembert's and Jourdain's Principles
25(2)
Mathematical Properties of the Descriptor Form
27(11)
The Index of the Descriptor Form
28(3)
Approaches for the Numerical Treatment of the Descriptor Form
31(2)
Consistency
33(2)
Existence and Uniqueness of Solutions
35(2)
Structures of the Index 1 Equations
37(1)
Practical Aspects of MBS
38(4)
Non-Smooth Models
39(1)
Multibody Formalisms
40(2)
Advantages of the Descriptor Form
42(4)
An Example from Engineering
43(1)
Minimal Model
43(2)
Descriptor Model
45(1)
Choice of coordinates
46(3)
Relative Coordinates
46(2)
Reference Point Coordinates
48(1)
Natural Coordinates
48(1)
Mixed Coordinates
49(1)
Interdependence of Modeling and Simulation
49(5)
Standard Approach: Forward Dynamics Simulation
50(1)
A New Approach: Inverse Dynamics Simulation
51(3)
A New Technique for Modeling of Universal Joints
54(3)
A Standard Model for Universal Joints
55(1)
A New Model for Universal Joints
56(1)
Summary of the Properties of MBS
57(4)
Software Engineering in Scientific Computing
61(38)
Application Oriented Scientific Software
63(5)
The Software Crisis
63(2)
Implications of the Research Factor
65(1)
Implications of Application Orientedness
66(1)
Scientific Software Products and Feasibility Engineering
66(2)
Complex Systems
68(5)
Characteristics of Complex Systems
68(2)
Key Factors for Mastering Complexity
70(2)
The Meaning of Software Engineering
72(1)
Software Quality
73(7)
Criteria Pertaining to Product Operation
74(2)
Criteria Pertaining to Product Transition
76(1)
Criteria Pertaining to Product Revision
77(1)
Software Quality Assurance
78(2)
Programming in the Small
80(1)
Coding and Design
80(1)
Testing
81(1)
Programming in the Large
81(12)
The Classic Sequential Life Cycle Model
82(6)
Prototyping
88(2)
A Prototyping Oriented Life Cycle Model for Feasibility Engineering
90(3)
Summary: Peculiarities of Feasibility Engineering
93(1)
Implementation: The Scientific Software MBSSIM
94(1)
Module Structure of MBSSIM
95(2)
The User Interface of MBSSIM
97(2)
Mathematical Methods for MBS in Descriptor Form
99(144)
Adaptive Adams methods
101(16)
Basics
102(9)
Computational Formulae for Adaptive Adams Methods
111(4)
Solution of the Nonlinear Corrector Systems
115(2)
A New Strategy for Controlling Adaptivity
117(10)
Formulae for Constant Stepsize
118(2)
Practical Error Estimation
120(1)
Choosing a New Order
121(2)
Choosing a New Stepsize
123(4)
A Runge-Kutta-Starter for Adaptive Adams Methods
127(10)
Goals of Construction
129(2)
Construction of the Runge-Kutta-Starter
131(4)
Error Estimation and Stepsize Selection
135(1)
Summary
136(1)
A Numerical Comparison
137(3)
Inverse Dynamics Integration
140(19)
A Local Complexity Analysis
141(2)
Inverse Dynamics: Taking a Global Perspective
143(2)
Conclusions for Descriptor Models: O(nb) methods
145(4)
Inverse Dynamics Multistep Methods for MBS in Descriptor Form
149(2)
A Monitoring Strategy for Approximate Jacobians in Corrector Systems
151(8)
Exploiting the Optimization Superstructure
159(20)
The Schur Complement Method
161(1)
The Range Space Method for Multibody Simulation
161(3)
Null Space Methods for Multibody Simulation
164(2)
A Unified View of RSM and NSM
166(2)
The NSM Based on LQ-Factorization
168(1)
The NSM Based on LU-Factorization
169(3)
A Nonsymmetric NSM Based on LU-Factorization
172(2)
A Comparison of Complexity for Dense Linear Algebra Solvers
174(2)
A Numerical Comparison of Dense Linear Algebra Solvers
176(3)
Topological Solution Algorithms
179(15)
Graphs of MBS
179(1)
Solution of Closed Loop Systems
180(2)
Recursive Solution of the Open Chain System
182(2)
Ingredients of the Recursion
184(2)
A Topological Solver Based on NSM
186(2)
A Numerical Study for the Topological Solver Using the IR-chain
188(6)
Projection Methods for Constrained MBS
194(31)
The Drift Phenomenon
195(1)
Exploitation of Invariants
196(3)
Exploiting the Sequential Structure
199(3)
Projection in a Weighted Norm
202(4)
Projection by Simplified Newton Methods
206(4)
Projection by Generalized Gauss-Newton Methods
210(4)
Projection by Moore-Penrose Iterations
214(4)
Algorithms for Sequential Projection and Choice of Norm
218(5)
A Projection Algorithm for NSM in Error Norm
223(2)
Sensitivities for Discontinuous Descriptor Models
225(18)
Parameter Dependent Discontinuous Descriptor Models
226(1)
The BVP Approach for Parameter Identification of MBS in Descriptor Form
227(4)
Internal Numerical Differentiation for MBS
231(3)
Updating Sensitivity Information in the Presence of Discontinuities
234(4)
Numerical Results
238(5)
Applications
243(34)
5-Link Suspension in Natural Coordinates
243(18)
Tire Model and Road Models
246(2)
A Relative Coordinate Model
248(1)
A New Natural Coordinate Model
249(10)
Alternative models based on natural or mixed coordinates
259(1)
Simulation Results
260(1)
A Comparison of Multibody Integrators
261(7)
A Comparison on a Smooth Model
263(2)
A Comparison on a Non-Smooth Model
265(1)
The Effect of Discontinuities on Simulation
266(2)
A High-Voltage Transmission Line
268(9)
A New Model for the Insulator Chain
269(5)
A Comparison of Sparse Solvers
274(3)
Summary: The MBSSIM Scientific Software Project
277(16)
Summary of MBSSIM's Life Cycle to Date
278(12)
Problem Analysis and Planning: Application Oriented Scientific Computing in Technical Mechanics
278(1)
Requirements Analysis and Specification: Identifying the Mathematical Challenges and Planning Feasibility Engineering
279(3)
System and Component Design: Reflecting Practical Requirements in Mathematical Algorithms
282(3)
Coding and Testing of Components: Improvements through New Mathematical Technology
285(2)
Testing of the System: Solving Application Problems
287(2)
Use and maintenance: Facing New Challenges
289(1)
Conclusions and Future Prospects
290(3)
Odds and Ends 293(8)
Coefficients for Adaptive Adams methods
293(3)
Proof of the Local Convergence Theorems
296(5)
WWW Pointers 301(2)
MBSSIM User's Guide
301(1)
Visualization of Results
301(1)
Vehicle System Dynamics
301(2)
List of Figures 303(4)
List of Tables 307(2)
Bibliography 309(22)
Index 331

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