Author: Edward J. Haug
Publisher: Springer Science & Business Media
ISBN: 3642761593
Category : Technology & Engineering
Languages : en
Pages : 356
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Book Description
This book contains the edited versions of lectures and selected contributed papers presented at the NATO Advanced Research Workshop on Real-Time Integration Methods For Mechanical System Simulation, held in Snowbird, Utah, August 7-11, 1989. The Institute was attended by 42 participants from 9 countries, including leading mathematicians and engineers from universities, research institutions, and industry. The majority of participants presented either invited or contributed papers during the Institute, and everyone participated in lively discussions on scientific aspects of the program. The Workshop provided a forum for investigation of promising new directions for solution of differential-algebraic equations (DAE) of mechanical system dynamics by mathematicians and engineers from numerous schools of thought. The Workshop addressed needs and opportunities for new methods of solving of DAE of mechanical system dynamics, from the perspective of a broad range of engineering and scientific applications. Among the most exciting new applications addressed was real time computer simulation of mechanical systems that, for the first time in human history, permits operator-in-the-Ioop simulation of equipment that is controlled by the human; e.g., driving a vehicle, operating a space telerobot, operating a remote manipulator, and operating construction equipment. The enormous potential value of this new application and the fact that real-time numerical integration methods for DAE of mechanical system dynamics is the pacing problem to be solved in realizing this potential served to focus much of the discussion at the Workshop.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
This project focused on the numerical algorithms and analysis which are needed for the effective real-time simulation of mechanical systems. Real-time simulation of mechanical systems is needed in robotics, as well as in the design and simulation of vehicles, including automobiles, high-speed trains, tanks and construction equipment. A number of related projects were proposed which would enable improved capabilities for real-time simulation of systems from mechanics, and also of related electrical, chemical and power systems. Proposed research included analysis and numerical algorithm development addressing these issues: problem formulation and numerical stability, exploiting structure and parallelism, high-frequency oscillations, rank-deficient constraints, discontinuities and delays.
Author: Manuel F.O. Seabra Pereira
Publisher: Springer Science & Business Media
ISBN: 9401711100
Category : Technology & Engineering
Languages : en
Pages : 314
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Book Description
This volume contains the edited version of selected papers presented at the Nato Advanced Study Institute on "Computer Aided Analysis of Rigid and Flexible Mechanical Systems", held in Portugal, from the 27 June to 9 July, 1994. The present volume can be viewed as a natural extension of the material addressed in the Institute which was published by KLUWER in the NATO ASI Series, Vol. 268, in 1994. The requirements for accurate and efficient analysis tools for design of large and lightweight mechanical systems has driven a strong interest in the challenging problem of multibody dynamics. The development of new analysis and design formulations for multi body systems has been more recently motivated with the need to include general features such as: real-time simulation capabilities, active control of machine flexibilities and advanced numerical methods related to time integration of the dynamic systems equations. In addition to the presentation of some basic formulations and methodologies in dynamics of multibody systems, including computational aspects, major applications of developments to date are presented herein. The scope of applications is extended to vehicle dynamics, aerospace technology, robotics, mechanisms design, intermittent motion and crashworthiness analysis. Several of these applications are explored by many contributors with a constant objective to pace development and improve the dynamic performance of mechanical systems avoiding different mechanical limitations and difficult functional requirements, such as, for example, accurate positioning of manipulators.
Author: Petre Teodorescu
Publisher: John Wiley & Sons
ISBN: 1118614623
Category : Computers
Languages : en
Pages : 458
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Book Description
A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.
Author: J. C. Butcher
Publisher: John Wiley & Sons
ISBN: 1119121515
Category : Mathematics
Languages : en
Pages : 544
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Book Description
A new edition of this classic work, comprehensively revised to present exciting new developments in this important subject The study of numerical methods for solving ordinary differential equations is constantly developing and regenerating, and this third edition of a popular classic volume, written by one of the world’s leading experts in the field, presents an account of the subject which reflects both its historical and well-established place in computational science and its vital role as a cornerstone of modern applied mathematics. In addition to serving as a broad and comprehensive study of numerical methods for initial value problems, this book contains a special emphasis on Runge-Kutta methods by the mathematician who transformed the subject into its modern form dating from his classic 1963 and 1972 papers. A second feature is general linear methods which have now matured and grown from being a framework for a unified theory of a wide range of diverse numerical schemes to a source of new and practical algorithms in their own right. As the founder of general linear method research, John Butcher has been a leading contributor to its development; his special role is reflected in the text. The book is written in the lucid style characteristic of the author, and combines enlightening explanations with rigorous and precise analysis. In addition to these anticipated features, the book breaks new ground by including the latest results on the highly efficient G-symplectic methods which compete strongly with the well-known symplectic Runge-Kutta methods for long-term integration of conservative mechanical systems. This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.
Author: Ernst Hairer
Publisher: Springer Science & Business Media
ISBN: 3662050188
Category : Mathematics
Languages : en
Pages : 526
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Book Description
This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
Author: Jorge A.C. Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3211994610
Category : Technology & Engineering
Languages : en
Pages : 426
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Book Description
Multibody systems are used extensively in the investigation of mechanical systems including structural and non-structural applications. It can be argued that among all the areas in solid mechanics the methodologies and applications associated to multibody dynamics are those that provide an ideal framework to aggregate d- ferent disciplines. This idea is clearly reflected, e. g. , in the multidisciplinary applications in biomechanics that use multibody dynamics to describe the motion of the biological entities, in finite elements where multibody dynamics provides - werful tools to describe large motion and kinematic restrictions between system components, in system control where the methodologies used in multibody dynamics are the prime form of describing the systems under analysis, or even in many - plications that involve fluid-structure interaction or aero elasticity. The development of industrial products or the development of analysis tools, using multibody dynamics methodologies, requires that the final result of the devel- ments are the best possible within some limitations, i. e. , they must be optimal. Furthermore, the performance of the developed systems must either be relatively insensitive to some of their design parameters or be sensitive in a controlled manner to other variables. Therefore, the sensitivity analysis of such systems is fundamental to support the decision making process. This book presents a broad range of tools for designing mechanical systems ranging from the kinematic and dynamic analysis of rigid and flexible multibody systems to their advanced optimization.
Author: Sergio Blanes
Publisher: CRC Press
ISBN: 1482263440
Category : Mathematics
Languages : en
Pages : 233
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Book Description
Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
Author: Eric Todd Phipps
Publisher:
ISBN:
Category :
Languages : en
Pages : 514
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Book Description
A multiple shooting technique for computing periodic orbits in these systems is presented as well. This technique allows the approximation of periodic orbits using coarse discretizations and converges to the orbit on a fixed discretization. The technique is found to provide highly accurate approximations of periodic orbits. The method is applied to a simple model of bipedal walking studied in [CGMR01]. Results consistent with those found in [CGMR01] are obtained, providing independent verification of the claim of the existence of a stable walking motion in this system.
Author: K. E. Brenan
Publisher: SIAM
ISBN: 0898713536
Category : Mathematics
Languages : en
Pages : 261
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Book Description
This book describes some of the places where differential-algebraic equations (DAE's) occur.
