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Modelling and analysis of dynamical systems is a widespreadpractice as it is important for engineers to know how a givenphysical or engineering system will behave under specificcircumstances. This text provides a comprehensive and systematic introductionto the methods and techniques used for translating physicalproblems into mathematical language, focusing on both linear andnonlinear systems. Highly practical in its approach, with solvedexamples, summaries, and sets of problems for each chapter,Dynamics for Engineers covers all aspects of the modellingand analysis of dynamical systems. Key…mehr

Produktbeschreibung
Modelling and analysis of dynamical systems is a widespreadpractice as it is important for engineers to know how a givenphysical or engineering system will behave under specificcircumstances. This text provides a comprehensive and systematic introductionto the methods and techniques used for translating physicalproblems into mathematical language, focusing on both linear andnonlinear systems. Highly practical in its approach, with solvedexamples, summaries, and sets of problems for each chapter,Dynamics for Engineers covers all aspects of the modellingand analysis of dynamical systems. Key features: * Introduces the Newtonian, Lagrangian, Hamiltonian, and BondGraph methodologies, and illustrates how these can be effectivelyused for obtaining differential equations for a wide variety ofmechanical, electrical, and electromechanical systems. * Develops a geometric understanding of the dynamics of physicalsystems by introducing the state space, and the character of thevector field around equilibrium points. * Sets out features of the dynamics of nonlinear systems, such aslike limit cycles, high-period orbits, and chaotic orbits. * Establishes methodologies for formulating discrete-time models,and for developing dynamics in discrete state space. Senior undergraduate and graduate students in electrical,mechanical, civil, aeronautical and allied branches of engineeringwill find this book a valuable resource, as will lecturers insystem modelling, analysis, control and design. This text will alsobe useful for students and engineers in the field ofmechatronics.

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  • Produktdetails
  • Verlag: John Wiley & Sons
  • Seitenzahl: 294
  • Erscheinungstermin: 13.12.2005
  • Englisch
  • ISBN-13: 9780470868454
  • Artikelnr.: 37299730
Autorenporträt
Soumitro Banerjee, Associate Professor, Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India Soumitro Banerjee has been at the Indian Institute of Technology, in the Department of Electrical Engineering since 1985. He currently teaches courses on 'Dynamics of Physical Systems', 'Signals and Networks', 'Energy Resources and Technology', 'Fractals, Chaos and Dynamical Systems' and 'Nonconventional Electrical Power Generation'. His research interests include bifurcation theory and chaos, and he has written and co-written over 43 papers on these subjects.
Inhaltsangabe
Preface. I: OBTAINING DIFFERENTIAL EQUATIONS FOR PHYSICAL SYSTEMS. 1. Introduction to System Elements. 1.1 Introduction. 1.2 Chapter summary. 2. Obtaining Differential Equations for Mechanical Systems by the Newtonian Method. 2.1 The Configuration Space. 2.2 Constraints. 2.3 Differential Equations from Newtons Laws. 2.4 Practical Difficulties with the Newtonian Formalism. 2.5 Chapter Summary. 3. Differential Equations of Electrical Circuits from Kirchoff's Laws. 3.1 Kirchoff's Laws about Current and Voltage. 3.2 The Mesh Current and Node Voltage Methods. 3.3 Using Graph Theory to Obtain the Minimal Set of Equations. 3.4 Chapter Summary. 4. The Lagrangian Formalism. 4.1 Elements of the Lagrangian Approach. 4.2 Obtaining Dynamical Equations by Lagrangian Method. 4.3 The Principle of Least Action. 4.4 Lagrangian Method Applied to Electrical Circuits. 4.5 Systems with External Forces or Electromotive Forces. 4.6 Systems with Resistance or Friction. 4.7 Accounting for Current Sources. 4.8 Modeling Mutual Inductances. 4.9 A General Methodology for Electrical Networks. 4.10 Modeling Coulomb Friction. 4.11 Chapter Summary. 5. Obtaining First
Order Equations. 5.1 First
Order Equations from the Lagrangian Method. 5.2 The Hamiltonian Formalism. 5.3 Chapter Summary. 6. Unified Modelling of Systems Through the Language of Bond Graphs. 6.1 Introduction. 6.2 The Basic Concept. 6.3 One
port Elements. 6.4 The Junctions. 6.5 Junctions in Mechanical Systems. 6.6 Numbering of Bonds. 6.7 Reference Power Directions. 6.8 Two
port Elements. 6.9 The Concept of Causality. 6.10 Differential Causality. 6.11 Obtaining Differential Equations from Bond Graphs. 6.12 Alternative Methods of Creating System Bond Graphs. 6.13 Algebraic Loops. 6.14 Fields. 6.15 Activation. 6.16 Equations for Systems with Differential Causality. 6.17 Bond Graph Software. 6.18 Chapter Summary. II: SOLVING DIFFERENTIAL EQUATIONS AND UNDERSTANDING DYNAMICS. 7. Numerical Solution of Differential Equations. 7.1 The Basic Method, and the Techniques of Approximation. 7.2 Methods to Balance Accuracy and Computation Time. 7.3 Chapter Summary. 8. Dynamics in the State Space. 8.1 The State Space. 8.2 Vector Field. 8.3 Local Linearization Around Equilibrium Points. 8.4 Chapter Summary. 9. Solutions for a System of First
Order Linear Differential Equations. 9.1 Solution of a First
Order Linear Differential Equation. 9.2 Solution of a System of Two First
Order Linear Differential Equations. 9.3 Eigenvalues and Eigenvectors. 9.4 Using Eigenvalues and Eigenvectors for Solving Differential Equations 9.5 Solution of a Single Second Order Differential Equation. 9.6 Systems with Higher Dimensions. 9.7 Chapter Summary. 10. Linear Systems with External Input. 10.1 Constant external input. 10.2 When the forcing function is a square wave. 10.3 Sinusoidal forcing function. 10.4 Other forms of excitation function. 10.5 Chapter Summary. 11. Dynamics of Nonlinear Systems. 11.1 All systems of practical interest are nonlinear. 11.2 Vector Fields for Nonlinear Systems. 11.3 Attractors in nonlinear systems. 11.4 Different types of periodic orbits in a nonlinear system. 11.5 Chaos. 11.6 Quasiperiodicity. 11.7 Stability of limit cycles. 11.8 Chapter Summary. 12. Discrete
time Dynamical Systems. 12.1 The Poincaré Section. 12.2 Obtaining a discrete
time model. 12.3 Dynamics of Discrete
Time Systems. 12.4 One
dimensional maps. 12.5 Bifurcations. 12.6 Saddle
node bifurcation. 12.7 Period
doubling bifurcation. 12.8 Periodic windows. 12.9 Two
dimensional maps. 12.10 Bifurcations in 2
D discrete
time systems. 12.11 Global dynamics of discrete
time systems. 12.12 Chapter Summary. Index.