Applied Dynamics – With Applications to Multibody and Mechatronic Systems 

Applied Dynamics – With Applications to Multibody and Mechatronic Systems 
اسم المؤلف
Francis C. Moon 
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10 أكتوبر 2020
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Applied Dynamics – With Applications to Multibody and Mechatronic Systems
Francis C. Moon 

Cornell University
Contents
Preface
1 Dynamic Phenomena and Failures
1.1 Introduction, 1
1.2 What’s New in Dynamics? 2
1.3 Dynamic Failures, 13
1.4 Basic Paradigms in Dynamics, 19
1.5 Coupled and Complex Dynamic Phenomena, 31
1.6 Dynamics and Design, 32
1.7 Modern Physics of Dynamics and Gravity, 33
2 Basic Principles of Dynamics
2.1 Introduction, 36
2.2 Kinematics, 36
2.3 Equilibrium and Virtual Work, 42
2.4 Systems of Particles, 44
2.5 Rigid Bodies, 51
2.6 D’Alembert’s Principle, 54
2.7 The Principle of Virtual Power, 56
36vi CONTENTS
3 Kinematics
3.1 Introduction, 62
3.2 Angular Velocity, 64
3.3 Matrix Representation of Angular Velocity, 67
3.4 Kinematics Relative to Moving Coordinate Frames, 68
3.5 Constraints and Jacobians, 72
3.6 Finite Motions, 75
3.7 Transformation Matrices for General Rigid-body Motion, 83
3.8 Kinematic Mechanisms, 88
62
4 Principles of D’Alembert, Virtual Power, and Lagrange’s Equations 103
4.1 Introduction, 103
4.2 D’Alembert’s Principle, 107
4.3 Lagrange’s Equations, 116
4.4 The Method of Virtual Power, 133
4.5 Nonholonomic Constraints: Lagrange Multipliers, 146
4.6 Variational Principles in Dynamics: Hamilton’s Principle, 153
5 Rigid Body Dynamics
5.1 Introduction, 168
5.2 Kinematics of Rigid Bodies, 171
5.3 Newton-Euler Equations of Motion, 181
5.4 Lagrange’s Equations for a Rigid Body, 205
5.5 Principle of Virtual Power for a Rigid Body, 214
5.6 Nonholonomic Rigid Body Problems, 230
168
6 Introduction to Robotics and Multibody Dynamics
6.1 Introduction, 254
6.2 Graph Theory and Incidence Matrices, 258
6.3 Kinematics, 265
6.4 Equations of Motion, 269
254CONTENTS vii
6.5 Inverse Problems, 289
6.6 Impact Problems, 296
7 Orbital and Satellite Dynamics 325
7.1 Introduction, 325
7.2 Central-force Dynamics, 327
7.3 Two-body Problems, 338
7.4 Rigid-body Satellite Dynamics, 341
7.5 Tethered Satellites, 358
8 Electromechanical Dynamics: An Introduction to Mechatronics 374
8.1 Introduction and Applications, 374
8.2 Electric and Magnetic Forces, 376
8.3 Electromechanical Material Properties, 383
8.4 Dynamic Principles of Electromagnetics, 390
8.5 Lagrange’s Equations for Magnetic Systems, 395
8.6 Applications, 407
8.7 Control Dynamics, 416
9 Introduction to Nonlinear and Chaotic Dynamics
9.1 Introduction, 432
9.2 Nonlinear Resonance, 435
9.3 The Undampled Pendulum: Phase-plane Motions, 439
9.4 Self-excited Oscillations: Limit Cycles, 443
9.5 Flows and Maps: Poincare Sections, 446
9.6 Complex Dynamics in Rigid-body Applications, 458
432
Appendix A Second Moments of Mass for Selected Geometric
Objects
Appendix B Commercial Dynamic Analysis and Simulation
Software Codes
474
478
References 483
Index 487Applied Dynamics

Francis C. Moon

© 1998 by John Wiley & Sons, Inc.

INDEX
Cam mechanism. 209
Cantilevered beam. 459
Cantor sets. 450
Cartesian coordinates. 37. 39
Catenary, 155
Center of gravity, 348
Center of mass, 45
Acceleration. 39
angular, 70
centripetal, 39, 270, 284
Coriolis. 39. 270, 284
relative to moving coordinates, 68
ADAMS, 10.481
Angular acceleration, 70, 172
Angular momentum, 46. 48. 181, 188, 191, 328 Central-force motion, 29, 327
Centripetal acceleration, 39. 70, 284. 289
Chain:
about center of mass, 48, 183
conservation of, 50
Angular velocity, 64, 266, 281
Angular velocity matrix. 67
Apogee, 336, 364
Attitude stability, 347
Auto-lev, 479
4-bar closed, 93
open, 257
Chaos, magnetic levitation. 453
Chaos theory, 432, 433. 450
Chaotic bouncing, 310
Chaotic dynamics, 434
Charge, conservation of, 392
Charge density, 377
Chasle’s theorem. 75
Circuit elements, 390
Circuits, 390
Circular orbits. 329, 340
Cobweb diagram, 451
Coefficient of restitution, 297, 309
Comagnetic energy, 398
Comagnetic energy function, 399
Computer graphics, 81
Conic sections, 329, 330
Conservation laws, 50
angular momentum, 50
Back emf, 378, 405
Ball joint. 256
Barium titanate, 389
Bearing forces, 194
Bending-torsional oscillations. 458, 462
Bernoulli. Jean, 154
Bernoulli family, 154
Bifurcation diagram, 452
Brachistochrone. 154
Brahe, Tycho. 325
Branched system, 257
Buckling. 17
Calder, Alexander, 464
487488 INDEX
Conservation laws (Continued )
charge, 392
energy, 437
linear momentum, 50
Conservative forces. 122, 123. 128
Constraint equations, 105
Constraint force, 55
Constraints. 39, 72. 104
holonomic, 133, 149
Jacobian, 39
nonholonomic, 133. 146, 149
sliding knife-edge, 232
unimodal, 255
Control dynamics, 415
Control force. 422
Control law. 422
Coordinate systems, 281
Cartesian. 37
cylindrical. 37
path coordinates, 135
Copernicus, Nicolaus. 325
Coriolis, Gaspard-Gustave de, 39
Coriolis acceleration, 39, 70, 284. 289. 461
Cross products of inertia, 53, 185
Current density, 377
Cyclic coordinate, 130
Cylindrical coordinates. 37. 39
Electric force, 123, 328, 429
Electric permittivity, 383
Electric susceptibility, 383
Electromagnetic Lagrangian, 403
Electromagnetic levitation ( EML). 10, 419
Electromagnetic units, 377
Elliptic orbits, 334, 336
End-effector. 290
Energy, conservation of. 50, 125. 437
Energy methods, 103
Energy principle, 49
Energy-limited vibration excitation, 426
Eotvos, Roland, 326
Equations of motion:
global matrix, 277
for a multibody system. 269
numerical integration, 278
Escape velocity, 334
Euler, L., 155
Euler Angles, 176, 180
Euler-Lagrange equation, 155
Euler parameters, 78
Euler’s equations, 53, 191, 192
modified, 192, 198, 199
Euler’s theorem. 52, 64,75
Failures, dynamic, 13
Faraday-Henry law. 392
Fatigue failure, 14
Feigenbaum, Mitchel. 452
Finite motions, 75. 173
Finite rotation, 174
Finite rotation vector, 78
Finite transformation matrix, 229
Flows, 446
Flutter, 17
Flywheel. 198
Focus. 363
Four-bar linkage. 91
Fourier transform, 434
Force:
active, 111. 283
conservative, 122, 123, 128
elastic spring, 123
electric and magnetic, 376
gravity, 20, 123
permanent magnet, 425
wire element carrying current, 378
Fractals, 310, 448
Free wall tunnel, 346
Frequency. 23
Friction, 210, 242, 444
DADS, 10, 481
D’Alembert, Jean Le Rond. 54
D’Alembert’s principle, 54, 104, 107. 109, 114
DC motor. 426
Degrees of freedom, 104, 279
Denavit-Hartenberg notation, 293
Difference equations. 447
Diodes, 384, 386, 391
Directrix. 363
Divergence. 17
Duffing. G., 436
Duffing oscillator, 437, 438
Dynamics equations:
for electric and magnetic circuits. 390
Dual spin satellite, 355
Dynamic instabilities. 16, 17
Earnshaw’s theorem, 419
Earthquake excitation, 24, 130
Effective potential, 332, 334
Einstein, Albert, 33, 326
Electrical conductivity, 384
Electric charges, 364
Electric coenergy, 403
Electric displacement, 383
Electric field, 377 Galileo Galilei. 20, 154, 325INDEX 489
Gear-rattling chaos, 461
Gear transmission, 462, 463
Generalized coordinates, 281
Generalized forces, 127, 140. 208, 278
Generalized inertia force. 140
Generalized momentum, 118, 129
Generalized speeds. 140
Geosynchronous orbit, 331
Goddard, Robert, 346
Graph theory, 5, 255, 258
Gravitational torque. 347
Gravitons, 34
Gravity, 33, 123
Gravity force. 20, 123.332. 341
Gravity-grade tunnel. 344, 368
Gravity gradient stabilization. 347
Gyro. 196
Gyropendulum, 217
Gyroscopic dynamics. 25, 195
Gyroscopic effects, 28, 54
Gyrostats, 356
Inductor, 391
Inertia matrix. 185
Internal forces, 111
Inverse problems, robotics, 289, 317
Inverse square law, 29. 123, 328
Jacobi, K.G.J.. 41
Jacobian, 39, 55, 72, 266, 268, 281
Jacobian matrix, 41, 106
Jacobian vectors, 49, 287
Joints. 89, 256
ball, 256. 262
prismatic, 256
revolute, 256
screw, 256
spherical, 256
Jourdain, Philip E.B., 4. 133. 138, 232
Jourdain’s principle, 56, 269
Kane, Thomas, 4, 56, 139, 232, 269
Kane’s equations, 133. 140
Kellogg. 342
Kepler, Johannes, 29, 325
Kepler’s laws, 328, 329, 331
Kicked rotor, 455, 471
Kinematic chain, 89. 257
Kinematic pairs, 89, 256
Kinematic relations, 127. 176. 177, 207
Kinematics, 36, 62, 265
connected rigid bodies, 266
particle, 37
rigid body, 171
Kinetic energy. 49, 125. 128. 205
Kinetic sculpture. 464
Kirchhoff ‘s circuit laws. 381, 393, 402
Hamilton, William Rowan. 103
Hamilton’s principle, 153
Hard spring. 436
Henon map. 448, 450
Hertz impact, 308, 324
Hohmann, Walter. 336
Hohmann orbit transfer. 337. 338
Holonomic constraints. 127. 133, 149. See
also Constraints
Homogeneous solution. 23
Horseshoe maps, 448
Hubble telescope. 170, 238
Hyperbolic orbit, 334
Hyperion, 466. 471
Hysteretic effects, 438 Lagrange, Joseph Louis. 103. 116. 155
Lagrange multiplier. 146, 151, 153.233. 235
Lagrange points, 373
Lagrange’s equations, 116. 119, 125. 126.
129. 148. 333
electric field system, 401
magnetic systems, 395
nonholonomic problems. 148
rigid body, 205
Lagrangian, 129, 399
electromechanical system, 405
Least action, principle of, 156
Leibniz, G.W., 323
Lenz’s law, 378
Levitation, 10. 198, 376
active controlled magnetic, 419
rare-earth magnet, 388
superconducting coil. 411
Ignorable coordinate. 130
Impact, 296, 300
central, 296
chaos, 311
elastic theory, 307
planar, 304
Poisson law, 297, 298
rigid body. 306
single-body, 305
Impact print hammer, 469
Impact times, 309
Impulse, impact force, 297
Incidence matrix, 258, 260, 262, 311
Inductance, 393, 397
mutual. 397
self, 397490 INDEX
Limit cycles, 443
Linear electric actuator, 406
Linear momentum. 46
conservation law, 50, 302
Linear oscillator. 436
Load line. 426
Lorenz, Edward. 434
Lyapunov exponent. 435
Mechanisms, 88
Artobolevsky, 6. 63
four-bar linkage. 91
four-bar spherical, 6
multiple bar dwell. 6
Reuleaux, 62
slider crank, 91. 169
Mechatronics, 9, 374
MEMS, 9, 11, 372, 406.413. 431
Machine noise, 298 Microelectromechanical accelerometer.
MACSYMA. 10
Mag-Lev, 9, 10, 17, 374. 394. See Levitation;
Magnetic levitation
Magnetic accelerator, 381
Magnetic actuator, 394
Magnetic bearings, superconducting.
413
Microelectromechanical systems, 374, 413.
See also MEMS
Moment of force, 47
Moment of inertia. 51, 53, 185
Momentum:
angular, 46
generalized, 129
linear
. 46
Motion-induced voltages. 378. See Back emf
Movie subroutines, MATLAB. 230
Multibody codes, 9. 258. 481. See also
ADAMS; Auto-lev; DADS; Working
model
Multibody dynamics. 4, 86, 254
198
Magnetic energy, 395, 408
Magnetic field. 378
Magnetic field density, 377
Magnetic flux, 392. 421
Magnetic flux linkage. 392, 397
Magnetic force. 123. 379, 397. 399
Magnetic forming, 382
Magnetic hammer. 407
Magnetic levitation. 10
rare-earth magnet, 388. See also Levitation
tunnel train. 346
Magnetic rail guns, 382
Magnetic reluctance, 421
Magnetic stress. 421
Magnetic susceptibility. 384
Magnetic thrust bearing. 198
Magnetization, 383
Magnetization curve. 385. 425
MAPLE, 10.479
Maps. 446
one-dimensional, 450
Mass drivers. 407
Mass matrix, 269
Mass moments. 183
MATHEMATICA, 10, 61, 92, 143. 479
MATLAB, 10, 81, 100, 101, 120. 230, 231,
240, 242. 366, 367, 409, 452. 480
Natural frequency. 437
NEWEUL, 480
Newton. Isaac. 2. 29, 33. 325
Newton-Euler equations. 19, 181.224
Newton law of impact. 296. 297
Newton’s law. 19. 47
third law. 270
Newton’s Principia. 2, 154
Nonholonomic constraints, 133, 146. 147.
148. 221
Nonholonomic problem, 5, 149. 230, 252
Nonlinear dynamics, 2. 43. 432. 434
Nonlinear oscillator. 436
Nonlinear resonance. 438
Numerical integration, equations of motion.
278
Octoberfest. 316
Orbits, 30, 329, 334, 367, 370, 373
Orbit-to-orbit transfer, 336
Orthogonal matrix, 173
Oscillations, self-excited, 443
Matrix:
angular velocity. 67
finite rotation, 77. 78
identity, 76
inertia. 185
mass, 269, 273
notation, 75
orthogonal. 76
4 X 4 transformation, 85
Maxwell. James Clerk, 34. 390
Maxwell’s equations, 390
Parabolic orbit. 334
Parallel axes theorem, 185
Partial velocities, 140
Particles, system of. 111, 126
Particular solution. 23
Path coordinates. 135INDEX 491
satellite dynamics, 341
Robot arm, three link, 285
Robot manipulator arm, 8. 255, 280. 290, 417
Robotic manipulators, serial-link, 274
Robotics, 254, 289
Rolling:
disc, stability of. 226
wheel, 149, 222
Rolling constraint. 221
Rotation. 52
Rotation induced stiffness, 212
Rotation matrix. 173
Rotation rate vector, 51. 171
Rotation transformation. 77
Routhian, 333
Pendulum, 20, 117, 141. 189, 241, 323, 439.
440, 442
double, 144, 321
Perigee, 336, 364
Period doubling. 435, 450. 472
Permanent magnetic material, 384
Perturbation theory, 203, 226
Pfeiffer, F.. 462
Phase plane, 25, 439
Piezoelectric:
bender actuator, 389
stack actuator, 389
Piezoelectric materials. 388
BaT;03, 389
PVDF, 389
PZT, 389
Planetary gears, 166
Planetary parameters, 335
Poincare, Henri, 3. 434, 447
Poincare map. 446, 448, 457
Poinsott ellipsoid, 204
Polar coordinates, 29
Polyvinyl difluoride (PVDF). 389
Position vector. 37
Potential energy, 50, 122. 343
Potential function, 332
Precession, 196
Principal axes, 185
Principal inertias, 53, 185
Printer mechanism, 468
Prismatic joint, 89, 256
Projection vectors, 221, 281
Pro/MECHANICA MOTION, 481
Pseudo phase plane, 470
PZT. 389
Saddle points, 441, 442
Satellite, 94, 186, 241.326. 366
deployment, 70
dumbbell, 351
four-mass cross, 353
Hubble. 170
stability of dumbbell. 351
tethered, 358
Scalar triple product. 207
Screw joint. 256
Second moments of mass, 185, 474
Seismograph, 399
Ship, roll dynamics, 469
Sierpinski carpet, 472
Simulation and animation software, 228. 478
Singular points. 93
Slider crank mechanism. 5, 91, 92, 169
Soft spring, 436
Solar panel, 71, 94, 326
Solar system satellite. 336
Solitons, 473
SOPHIA. 480
Spacecraft. 239, 326
Hubble, 170
Stability:
dumbbell satellite, 351
rigid body rotation, 201, 202
rotating pendulum. 245
spinning satellite, 244
vehicle skid. 237
State feedback control, 416
State vector, 25
Stick-slip, 444
Strange attractor. 434
Superconductors. 386. 387
high-temperature, 387
System identification:
linear systems, 13
nonlinear systems. 13
Quasi-periodic motions. 434. 446
Rare-earth magnet, 385
Rayleigh dissipation function, 126, 129,
403
Rectangular coordinates, 38
Relative permeability, 384
Relaxation oscillations, 444
Resistivity, 384
Resistors. 384
Resonance. 23, 25
nonlinear. 438
Reuleaux, Franz, 5, 62
Revolute joints, 89, 256
Rickey, George, 464
Rigid body. 51. 168, 191.458
general motion of, 221
moment-free dynamics, 200
motion about a fixed point, 215492 INDEX
Vehicle stability, 232
Velocity, 38
Vibration absorber, 157
Vibration period, 437
Virtual displacement, 42
Virtual power, 56, 118, 133, 136, 143, 221, 224,
234, 273, 279
connected rigid bodies, 270
electromechanical systems, 396
general motion of a rigid body.
Tait-Bryan angles, 178
Tangent vectors, 139
Tinguely, Jean, 464
Three-body gravitational dynamics, 372
restricted, 373
Three-link planar manipulator, 86
Toys, 2
spinner, 250
Transfer orbit, 370
Transformation matrix. 76, 83, 178
Transformation matrices, 4 x 4, 86, 99, 293
Transistor, 391
Triple scalar product, 216
Triple vector product, 183
Two-body problems, 338
Two-link manipulator arm, 276, 289
Two-link mechanism. 74, 167, 239, 260, 268,
219
Newton-Euler Methods, comparison of.
221
rigid body, 214, 216
system of particles. 138
using MATHEMATICA, 143
Virtual velocities, 62, 103, 138
Virtual work, 42, 55. 345
Vitesse virtuelle, 154. See also Virtual
velocities
Voice coil actuator, 379
321
Unimodal constraints, 255
Vehicle dynamics, 178
Vehicle skid, 252
stability of. 237
Wild mouse, 316
Working model, 10, 12. 482
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