Ordinary Differential Equations And Mechanical Systems PDF Download
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Author | : Jan Awrejcewicz |
Publisher | : Springer |
Total Pages | : 621 |
Release | : 2014-09-17 |
Genre | : Mathematics |
ISBN | : 3319076590 |
Download Ordinary Differential Equations and Mechanical Systems Book in PDF, ePub and Kindle
This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
Author | : Wei-Chau Xie |
Publisher | : Cambridge University Press |
Total Pages | : 567 |
Release | : 2010-04-26 |
Genre | : Technology & Engineering |
ISBN | : 1139488163 |
Download Differential Equations for Engineers Book in PDF, ePub and Kindle
Xie presents a systematic introduction to ordinary differential equations for engineering students and practitioners. Mathematical concepts and various techniques are presented in a clear, logical, and concise manner. Various visual features are used to highlight focus areas. Complete illustrative diagrams are used to facilitate mathematical modeling of application problems. Readers are motivated by a focus on the relevance of differential equations through their applications in various engineering disciplines. Studies of various types of differential equations are determined by engineering applications. Theory and techniques for solving differential equations are then applied to solve practical engineering problems. A step-by-step analysis is presented to model the engineering problems using differential equations from physical principles and to solve the differential equations using the easiest possible method. This book is suitable for undergraduate students in engineering.
Author | : H.Y. Hu |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2013-03-09 |
Genre | : Technology & Engineering |
ISBN | : 3662050307 |
Download Dynamics of Controlled Mechanical Systems with Delayed Feedback Book in PDF, ePub and Kindle
Recent years have witnessed a rapid development of active control of various mechanical systems. With increasingly strict requirements for control speed and system performance, the unavoidable time delays in both controllers and actuators have become a serious problem. For instance, all digital controllers, analogue anti aliasing and reconstruction filters exhibit a certain time delay during operation, and the hydraulic actuators and human being interaction usually show even more significant time delays. These time delays, albeit very short in most cases, often deteriorate the control performance or even cause the instability of the system, be cause the actuators may feed energy at the moment when the system does not need it. Thus, the effect of time delays on the system performance has drawn much at tention in the design of robots, active vehicle suspensions, active tendons for tall buildings, as well as the controlled vibro-impact systems. On the other hand, the properly designed delay control may improve the performance of dynamic sys tems. For instance, the delayed state feedback has found its applications to the design of dynamic absorbers, the linearization of nonlinear systems, the control of chaotic oscillators, etc. Most controlled mechanical systems with time delays can be modeled as the dynamic systems described by a set of ordinary differential equations with time delays.
Author | : Roger F. Gans |
Publisher | : Springer |
Total Pages | : 448 |
Release | : 2014-09-02 |
Genre | : Technology & Engineering |
ISBN | : 3319083716 |
Download Mechanical Systems Book in PDF, ePub and Kindle
This essential textbook concerns analysis and control of engineering mechanisms, which includes almost any apparatus with moving parts used in daily life, from musical instruments to robots. A particular characteristic of this book is that it presents with considerable breadth and rigor both vibrations and controls. Many contemporary texts combine both of these topics in a single, one term course. This text supports the more favorable circumstance where the material is covered in a one year sequence contains enough material for a two semester sequence, but it can also be used in a single semester course combining two topics. “Mechanical Systems: A Unified Approach to Vibrations and Controls” presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text.
Author | : Bill Goodwine |
Publisher | : Springer Science & Business Media |
Total Pages | : 762 |
Release | : 2010-11-11 |
Genre | : Mathematics |
ISBN | : 1441979190 |
Download Engineering Differential Equations Book in PDF, ePub and Kindle
This book is a comprehensive treatment of engineering undergraduate differential equations as well as linear vibrations and feedback control. While this material has traditionally been separated into different courses in undergraduate engineering curricula. This text provides a streamlined and efficient treatment of material normally covered in three courses. Ultimately, engineering students study mathematics in order to be able to solve problems within the engineering realm. Engineering Differential Equations: Theory and Applications guides students to approach the mathematical theory with much greater interest and enthusiasm by teaching the theory together with applications. Additionally, it includes an abundance of detailed examples. Appendices include numerous C and FORTRAN example programs. This book is intended for engineering undergraduate students, particularly aerospace and mechanical engineers and students in other disciplines concerned with mechanical systems analysis and control. Prerequisites include basic and advanced calculus with an introduction to linear algebra.
Author | : Edward J. Haug |
Publisher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2013-06-29 |
Genre | : Technology & Engineering |
ISBN | : 3642761593 |
Download Real-Time Integration Methods for Mechanical System Simulation Book in PDF, ePub and Kindle
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 | : Gerald Teschl |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 2012-08-30 |
Genre | : Mathematics |
ISBN | : 0821883283 |
Download Ordinary Differential Equations and Dynamical Systems Book in PDF, ePub and Kindle
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Author | : J. C. Butcher |
Publisher | : John Wiley & Sons |
Total Pages | : 544 |
Release | : 2016-08-05 |
Genre | : Mathematics |
ISBN | : 1119121523 |
Download Numerical Methods for Ordinary Differential Equations Book in PDF, ePub and Kindle
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 | : Thomas Witelski |
Publisher | : Springer |
Total Pages | : 309 |
Release | : 2015-09-18 |
Genre | : Mathematics |
ISBN | : 3319230425 |
Download Methods of Mathematical Modelling Book in PDF, ePub and Kindle
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Author | : Stephen L. Campbell |
Publisher | : Princeton University Press |
Total Pages | : 445 |
Release | : 2011-10-14 |
Genre | : Mathematics |
ISBN | : 1400841321 |
Download Introduction to Differential Equations with Dynamical Systems Book in PDF, ePub and Kindle
Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.