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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.

Taal / Language : English

Inhoudsopgave:
Preface xi
I Obtaining differential equations for physical systems 1(150)
 1 Introduction to System Elements
3(8)
 1.1 Introduction
3(6)
 1.1.1 The inertial element
3(2)
 1.1.2 The compliant element
5(1)
 1.1.3 The resistive element
6(1)
 1.1.4 The voltage source and externally impressed force
7(1)
 1.1.5 The current source and externally impressed sources of flow
8(1)
 1.2 Chapter Summary
9(1)
10(1)
 2 Obtaining Differential Equations for Mechanical Systems by the Newtonian Method
11(10)
 2.1 The Configuration Space
12(1)
 2.2 Constraints
13(2)
 2.3 Differential Equations from Newton`s Laws
15(1)
 2.4 Practical Difficulties with the Newtonian Formalism
16(1)
 2.5 Chapter Summary
17(1)
18(1)
 Problems
18(3)
 3 Differential Equations of Electrical Circuits from Kirchoff`s Laws
21(24)
 3.1 Kirchoff`s Laws about Current and Voltage
21(2)
 3.2 The Mesh Current and Node Voltage Methods
23(5)
 3.3 Using Graph Theory to Obtain the Minimal Set of Equations
28(13)
 3.3.1 Kirchoff`s laws relating to loops and cutsets
29(1)
 3.3.2 Tree and co-tree
30(1)
 3.3.3 The independent KCL and KVL equations
31(1)
 3.3.4 The choice of the state variables
31(1)
 3.3.5 Derivation of differential equations
32(9)
 3.4 Chapter Summary
41(1)
42(1)
 Problems
42(3)
 4 The Lagrangian Formalism
45(40)
 4.1 Elements of the Lagrangian Approach
46(7)
 4.1.1 Motivation
46(1)
 4.1.2 The concept of admissible motions
46(2)
 4.1.3 The generalized coordinates
48(2)
 4.1.4 Dynamical equations in terms of energies
50(3)
 4.2 Obtaining Dynamical Equations by Lagrangian Method
53(9)
 4.3 The Principle of Least Action
62(5)
 4.4 Lagrangian Method Applied to Electrical Circuits
67(1)
 4.5 Systems with External Forces or Electromotive Forces
68(2)
 4.6 Systems with Resistance or Friction
70(4)
 4.7 Accounting for Current Sources
74(1)
 4.8 Modelling Mutual Inductances
75(2)
 4.9 A General Methodology for Electrical Networks
77(1)
 4.10 Modelling Coulomb Friction
78(2)
 4.11 Chapter Summary
80(1)
80(1)
 Problems
81(4)
 5 Obtaining First-order Equations
85(20)
 5.1 First-order Equations from the Lagrangian Method
85(3)
 5.2 The Hamiltonian Formalism
88(12)
 5.3 Chapter Summary
100(1)
 Problems
101(4)
 6 Unified Modelling of Systems Through the Language of Bond Graphs
105(46)
 6.1 Introduction
105(1)
 6.2 The Basic Concept
106(1)
 6.3 One-port Elements
106(2)
 6.4 The Junctions
108(2)
 6.5 Junctions in Mechanical Systems
110(2)
 6.6 Numbering of Bonds
112(1)
 6.7 Reference Power Directions
112(4)
 6.8 Two-port Elements
116(2)
 6.9 The Concept of Causality
118(3)
 6.10 Differential Causality
121(2)
 6.11 Obtaining Differential Equations from Bond Graphs
123(5)
 6.12 Alternative Methods of Creating System Bond Graphs
128(4)
 6.12.1 Electrical systems
129(1)
 6.12.2 Mechanical systems
130(2)
 6.13 Algebraic Loops
132(2)
 6.14 Fields
134(4)
 6.15 Activation
138(3)
 6.16 Equations for Systems with Differential Causality
141(1)
 6.17 Bond Graph Software
142(2)
 6.18 Chapter Summary
144(1)
145(1)
 Problems
145(6)
II Solving differential equations and understanding dynamics 151(126)
 7 Numerical Solution of Differential Equations
153(8)
 7.1 The Basic Method and the Techniques of Approximation
153(5)
 7.1.1 The Euler method
154(1)
 7.1.2 The trapezoidal rule
155(1)
 7.1.3 The fourth-order Runge-Kutta formula
156(2)
 7.2 Methods to Balance Accuracy and Computation Time
158(1)
 7.3 Chapter Summary
159(1)
159(1)
 Problems
160(1)
 8 Dynamics in the State Space
161(8)
 8.1 The State Space
162(1)
 8.2 Vector Field
163(1)
 8.3 Local Linearization Around Equilibrium Points
163(3)
 8.4 Chapter Summary
166(1)
 Problems
166(3)
 9 Solutions for a System of First-order Linear Differential Equations
169(28)
 9.1 Solution of a First-order Linear Differential Equation
170(1)
 9.2 Solution of a System of Two First-order Linear Differential Equations
171(1)
 9.3 Eigenvalues and Eigenvectors
172(1)
 9.4 Using Eigenvalues and Eigenvectors for Solving Differential Equations
173(13)
 9.4.1 Eigenvalues real and distinct
174(3)
 9.4.2 Eigenvalues complex conjugate
177(3)
 9.4.3 Eigenvalues purely imaginary
180(4)
 9.4.4 Eigenvalues real and equal
184(2)
 9.5 Solution of a Single Second-order Differential Equation
186(3)
 9.6 Systems with Higher Dimensions
189(5)
 9.7 Chapter Summary
194(1)
195(1)
 Problems
195(2)
 10 Linear Systems with External Input
197(22)
 10.1 Constant External Input
197(6)
 10.1.1 Constant voltage applied to an RL circuit
197(2)
 10.1.2 The concept of time constant
199(2)
 10.1.3 Constant voltage applied to an RC circuit
201(1)
 10.1.4 Constant voltage applied to an RLC circuit
202(1)
 10.2 When the Forcing Function is a Square Wave
203(1)
 10.3 Sinusoidal Forcing Function
204(9)
 10.3.1 First-order systems excited by sinusoidal source
204(6)
 10.3.2 Second-order system excited by sinusoidal source
210(3)
 10.4 Other Forms of Excitation Function
213(2)
 10.5 Chapter Summary
215(1)
215(1)
 Problems
215(4)
 11 Dynamics of Nonlinear Systems
219(22)
 11.1 All Systems of Practical Interest are Nonlinear
219(1)
 11.2 Vector Fields for Nonlinear Systems
220(7)
 11.3 Attractors in Nonlinear Systems
227(1)
 11.4 Limit Cycle
228(1)
 11.5 Different Types of Periodic Orbits in a Nonlinear System
229(2)
 11.6 Chaos
231(3)
 11.7 Quasiperiodicity
234(2)
 11.8 Stability of Limit Cycles
236(1)
 11.9 Chapter Summary
236(1)
237(1)
 Problems
237(4)
 12 Discrete-time Dynamical Systems
241(36)
 12.1 The Poincaré Section
241(4)
 12.2 Obtaining a Discrete-time Model
245(3)
 12.3 Dynamics of Discrete-time Systems
248(1)
 12.4 One-dimensional Maps
248(7)
 12.5 Bifurcations
255(1)
256(2)
 12.7 Period-doubling Bifurcation
258(2)
 12.8 Periodic Windows
260(1)
 12.9 Two-dimensional Maps
261(3)
 12.10 Bifurcations in 2-D Discrete-time Systems
264(5)
 12.11 Global Dynamics of Discrete-time Systems
269(3)
 12.12 Chapter Summary
272(1)
273(1)
 Problems
273(4)
Index 277
Extra informatie:
Paperback / softback
296 pagina's
Januari 2005
567 gram
247 x 167 x 17 mm
Wiley-Blackwell

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