Soumitro Banerjee

Dynamics for Engineers

• Broschiertes Buch

Produktbeschreibung

Thoroughly class-tested, this book focuses on the modelling and analysis of linear as well as nonlinear dynamical systems with emphasis on electrical, mechanical, and electromechanical systems. The readers are first introduced to the methods and techniques for translating a physical problem into mathematical language by formulating differential equations.

Nowtonian, Lagrangian, and Hamiltonian methods are introduced, along with the method of bond graphs. Solutions of differential equations, both by analytical as well as numerical methods then follow, with an emphasis on developing a geometric understanding of dynamics in the state space. As well as drawing from the methods used in the study of nonlinear dynamics, this text also illustrates the application of these methods in the context of engineering systems. This book also covers discrete-time dynamical systems and methods of analyzing discrete dynamics. Each chapter contains numerous solved examples, a summary, and a set of problems.

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Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 296
• Erscheinungstermin: 1. August 2005
• Englisch
• Abmessung: 244mm x 170mm x 16mm
• Gewicht: 545g
• ISBN-13: 9780470868447
• ISBN-10: 0470868449
• Artikelnr.: 14746928

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. 1 Introduction to System Elements. 1.1 Introduction. 1.2 Chapter
summary. 2 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 by 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 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. 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 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 Poincar¿e
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.