 اسم المؤلف
Adrian B. Biran, Moshe Breiner
التاريخ
4 سبتمبر 2017
المشاهدات
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سلسلة مايجب على كل مهندس معرفته عن الماتلاب والسميولينك
What Every Engineer Should Know about MATLAB and Simulink
Adrian B. Biran
With contributions by Moshe Breiner
Contents
Preface xv
I Introducing MATLAB 1
1 Introduction to MATLAB 3
1.1 Starting MATLAB 3
1.2 Using MATLAB as a simple calculator . 5
1.3 How to quit MATLAB 9
1.4 Using MATLAB as a scientific calculator 10
1.4.1 Trigonometric functions . 10
1.4.2 Inverse trigonometric functions . 13
1.4.3 Other elementary functions . 15
1.5 Arrays of numbers 16
1.6 Using MATLAB for plotting . 18
1.6.1 Annotating a graph . 20
1.7 Format . 21
1.8 Arrays of numbers 22
1.8.1 Array elements 22
1.8.2 Plotting resolution 23
1.8.3 Array operations . 24
1.9 Writing simple functions in MATLAB . 27
1.10 Summary . 31
1.11 Examples . 34
1.12 More exercises . 42
2 Vectors and matrices 47
2.1 Vectors in geometry . 48
2.1.1 Arrays of point coordinates in the plane 48
2.1.2 The perimeter of a polygon – for loops . 52
2.1.3 Vectorization . 55
2.1.4 Arrays of point coordinates in solid geometry . 56
2.1.5 Geometrical interpretation of vectors 61
2.1.6 Operating with vectors 63
2.1.7 Vector basis 65
2.1.8 The scalar product 66
2.2 Vectors in mechanics . 69
ixx What every engineer should know about MATLABand Simulink
2.2.1 Forces. The resultant of two or more forces 69
2.2.2 Work as a scalar product 72
2.2.3 Velocities. Composition of velocities 72
2.3 Matrices 73
2.3.1 Introduction – the matrix product . 73
2.3.2 Determinants . 77
2.4 Matrices in geometry . 78
2.4.1 The vector product. Parallelogram area 78
2.4.2 The scalar triple product. Parallelepiped volume . 80
2.5 Transformations 82
2.5.1 Translation — Matrix addition and subtraction 82
2.5.2 Rotation 83
2.5.3 Homogeneous coordinates 84
2.6 Matrices in Mechanics 88
2.6.1 Angular velocity . 88
2.6.2 Center of mass 89
2.6.3 Moments as vector products . 91
2.7 Summary . 93
2.8 More exercises . 98
3 Equations 103
3.1 Introduction 103
3.2 Linear equations in geometry 103
3.2.1 The intersection of two lines . 103
3.2.2 Cramer’s rule . 104
3.2.3 MATLAB’s solution of linear equations 105
3.2.4 An example of an ill-conditioned system 107
3.2.5 The intersection of three planes . 109
3.3 Linear equations in statics 109
3.3.1 A simple beam 109
3.4 Linear equations in electricity 112
3.4.1 A DC circuit . 112
3.4.2 The method of loop currents 114
3.5 On the solution of linear equations . 116
3.5.1 Homogeneous linear equations 116
3.5.2 Overdetermined systems — least-squares solution . 119
3.5.3 Underdetermined system . 123
3.5.4 A singular system . 126
3.5.5 Another singular system . 128
3.6 Summary 1 132
3.7 More exercises . 134
3.8 Polynomial equations . 135
3.8.1 MATLAB representation of polynomials 135
3.8.2 The MATLAB root function 135
3.8.3 The MATLAB function conv 137Table of Contents xi
3.9 Iterative solution of equations 143
3.9.1 The Newton-Raphson method 143
3.9.2 Solving an equation with the command fzero . 147
3.10 Summary 2 148
3.11 More exercises . 149
4 Processing and publishing the results 151
4.1 Copy and paste 151
4.2 Diary 152
4.3 Exporting and processing figures 152
4.4 Interpolation . 153
4.4.1 Interactive plotting and curve fitting 153
4.5 The MATLABspline function . 157
4.6 Importing data from Excel – histograms . 165
4.7 Summary . 167
4.8 Exercises 169
II Programming in MATLAB 171
5 Some facts about numerical computing 173
5.1 Introduction 173
5.2 Computer-aided mistakes 174
5.2.1 A loop that does not stop 175
5.2.2 Errors in trigonometric functions 176
5.2.3 An unexpected root . 176
5.2.4 Other unexpected roots . 178
5.2.5 Accumulating errors . 179
5.3 Computer representation of numbers 180
5.4 The set of computer numbers 184
5.5 Roundoff 186
5.6 Roundoff errors 187
5.7 Computer arithmetic . 191
5.8 Why the examples in Section 5.2 failed . 193
5.8.1 Absorbtion 193
5.8.2 Correcting a non-terminating loop . 194
5.8.3 Second-degree equation . 194
5.8.4 Unexpected polynomial roots 196
5.9 Truncation error . 199
5.10 Complexity 202
5.10.1 Definition, examples . 202
5.11 Horner’s scheme 205
5.12 Problems that cannot be solved . 206
5.13 Summary . 208
5.14 More examples 209
5.15 More exercises . 211xii What every engineer should know about MATLABand Simulink
6 Data types and object-oriented programming 215
6.1 Structures . 216
6.1.1 Where structures can help 216
6.1.2 Working with structures . 217
6.2 Cell arrays . 219
6.3 Classes and object-oriented programming . 221
6.3.1 What is object-oriented programming? . 221
6.3.2 Calculations with units 222
6.3.3 Defining a class 224
6.3.4 Defining a subclass 229
6.3.5 Calculating with electrical units . 233
6.4 Summary . 238
6.5 Exercises 240
III Progressing in MATLAB 243
7 Complex numbers 245
7.1 The introduction of complex numbers . 245
7.2 Complex numbers in MATLAB . 245
7.3 Geometric representation 248
7.4 Trigonometric representation 250
7.5 Exponential representation . 250
7.6 Functions of complex variables . 253
7.7 Conformal mapping . 255
7.8 Phasors 259
7.8.1 Phasors 259
7.8.2 Phasors in mechanics . 261
7.8.3 Phasors in electricity . 265
7.9 An application in mechanical engineering — a mechanism 271
7.9.1 A four-link mechanism 271
7.9.2 Displacement analysis of the four-link mechanism . 272
7.9.3 A MATLAB function that simulates the motion of the
four-link mechanism . 274
7.9.4 Animation . 277
7.9.5 A variant of the function FourLink . 278
7.10 Summary . 281
7.11 Exercises 283
8 Numerical integration 287
8.1 Introduction 287
8.2 The trapezoidal rule . 288
8.2.1 The formula 288
8.2.2 The MATLAB trapz function . 289
8.3 Simpson’s rule . 290
8.3.1 The formula 290Table of Contents xiii
8.3.2 A function that implements Simpson’s rule 292
8.4 The MATLAB quadl function 293
8.5 Symbolic calculation of integrals 295
8.6 Summary . 297
8.7 Exercises 298
9 Ordinary differential equations 301
9.1 Introduction 301
9.2 Numerical solution of ordinary differential equations . 301
9.2.1 Cauchy form . 301
9.3 Numerical solution of ordinary differential equations . 302
9.3.1 Specifying the times of the solution . 305
9.3.2 Using alternative odesolvers . 306
9.3.3 Passing parameters to the model 306
9.4 Alternative strategies to solve ordinary differential equations . 310
9.4.1 Runge–Kutta methods 312
9.4.2 Predictor-corrector methods . 315
9.4.3 Stiff systems 316
9.5 Conclusion: How to choose the odesolver 323
9.6 Exercises 324
10 More graphics 327
10.1 Introduction 327
10.2 Drawing at scale . 327
10.3 The cone surface and conic sections . 330
10.3.1 The cone surface . 330
10.3.2 Conic sections . 332
10.3.3 Developing the cone surface . 336
10.3.4 A helicoidal curve on the cone surface . 337
10.3.5 The listing of functions developed in this section . 338
10.4 GUIs – graphical user interfaces . 343
10.5 Summary . 355
10.6 Exercises 356
11 An introduction to Simulink 359
11.1 What is simulation? . 359
11.2 Beats 360
11.3 A model of the momentum law . 366
11.4 Capacitor discharge 370
11.5 A mass–spring–dashpot system . 376
11.6 A series RLC circuit . 380
11.7 The pendulum 383
11.7.1 The mathematical and the physical pendulum . 383
11.7.2 The phase plane . 387
11.7.3 Running the simulation from a script file 39111.8 Exercises 393
12 Applications in the frequency domain 395
12.1 Introduction 395
12.2 Signals . 395
12.3 A short introduction to the DFT 398
12.4 The power spectrum . 400
12.5 Trigonometric expansion of a signal . 407
12.6 High frequency signals and aliasing . 410
12.7 Bode plot . 412
12.8 Summary . 414
12.9 Exercises 415
Answers to selected exercises 417
Bibliography 423
Index
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