Soumitro Banerjee

Dynamics for Engineers (eBook, PDF)

• Format: PDF

Produktbeschreibung

Modelling and analysis of dynamical systems is a widespread practice as it is important for engineers to know how a given physical or engineering system will behave under specific circumstances. This text provides a comprehensive and systematic introduction to the methods and techniques used for translating physical problems into mathematical language, focusing on both linear and nonlinear systems. Highly practical in its approach, with solved examples, summaries, and sets of problems for each chapter, Dynamics for Engineers covers all aspects of the modelling and analysis of dynamical systems. Key features: * Introduces the Newtonian, Lagrangian, Hamiltonian, and Bond Graph methodologies, and illustrates how these can be effectively used for obtaining differential equations for a wide variety of mechanical, electrical, and electromechanical systems. * Develops a geometric understanding of the dynamics of physical systems by introducing the state space, and the character of the vector field around equilibrium points. * Sets out features of the dynamics of nonlinear systems, such as like 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 engineering will find this book a valuable resource, as will lecturers in system modelling, analysis, control and design. This text will also be useful for students and engineers in the field of mechatronics.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 294
• Erscheinungstermin: 13. Dezember 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.