Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications

✍ Scribed by Reza N. Jazar

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Leaves: 1344
• Edition: 1
• Category: Library

✦ Synopsis

According to the author and reviewers, more than 50% of the material taught in courses such as Advanced Dynamics, Mutibody Dynamics, and Spacecraft Dynamics is common to one another. Where graduate students in Mechanical and Aerospace Engineering may have the potential to work on projects that are related to any of the engineering disciplines, they have not been exposed to enough applications in both areas for them to use this information in the real world. This book bridges the gap between rigid body, multibody, and spacecraft dynamics for graduate students and specialists in mechanical and aerospace engineering. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications across different engineering disciplines.The book begins with a review on coordinate systems and particle dynamics which will teach coordinate frames. The transformation and rotation theory along with the differentiation theory in different coordinate frames will provides the required background to learn the rigid body dynamics based on Newton-Euler principles. Applications to this coverage can be found in vehicle dynamics, spacecraft dynamics, aircraft dynamics, robot dynamics, and multibody dynamics, each in a chapter. The Newton equations of motion will be transformed to Lagrange equation as a bridge to analytical dynamics. The methods of Lagrange and Hamilton will be applied on rigid body dynamics. Finally through the coverage of special applications this text provides understanding of advanced systems without restricting itself to a particular discipline. The author will provide a detailed solutions manual and powerpoint slides as ancillaries to this book.

✦ Table of Contents

Advanced Dynamics......Page 5
Contents......Page 9
Preface......Page 15
Part I Fundamentals......Page 21
1.1.1 Triad......Page 23
1.1.2 Coordinate Frame and Position Vector......Page 24
1.1.3 Vector Definition......Page 30
1.2.1 Vector Addition......Page 32
1.2.2 Vector Multiplication......Page 37
1.2.3 Index Notation......Page 46
1.3.1 Orthogonality Condition......Page 51
1.3.2 Unit Vector......Page 54
1.3.3 Direction of Unit Vectors......Page 56
1.4 Differential Geometry......Page 57
1.4.1 Space Curve......Page 58
1.4.2 Surface and Plane......Page 63
1.5.1 Vector Function and Derivative......Page 66
1.5.2 Velocity and Acceleration......Page 71
1.5.3 Natural Coordinate Frame......Page 74
1.6 Fields......Page 97
1.6.1 Surface and Orthogonal Mesh......Page 98
1.6.2 Scalar Field and Derivative......Page 105
1.6.3 Vector Field and Derivative......Page 112
Key Symbols......Page 120
Exercises......Page 123
2.1 Laws of Motion......Page 134
2.2 Equation of Motion......Page 139
2.2.1 Force and Moment......Page 140
2.2.2 Motion Equation......Page 145
2.3 Special Solutions......Page 151
2.3.1 Force Is a Function of Time, F = F(t)......Page 152
2.3.2 Force Is a Function of Position, F = F(x)......Page 161
2.3.3 Elliptic Functions......Page 168
2.3.4 Force Is a Function of Velocity, F = F(v)......Page 176
2.4.1 Spatial Integral: Work and Energy......Page 185
2.4.2 Temporal Integral: Impulse and Momentum......Page 196
2.5 Application of Dynamics......Page 208
2.5.1 Modeling......Page 209
2.5.2 Equations of Motion......Page 217
2.5.3 Dynamic Behavior and Methods of Solution......Page 220
2.5.4 Parameter Adjustment......Page 240
Key Symbols......Page 243
Exercises......Page 246
Part II Geometric Kinematics......Page 261
3.1 Cartesian Coordinate System......Page 263
3.2 Cylindrical Coordinate System......Page 270
3.3 Spherical Coordinate System......Page 283
3.4.1 Reciprocal Base Vectors......Page 289
3.4.2 Reciprocal Coordinate Frame......Page 298
3.4.3 Inner and Outer Vector Product......Page 305
3.4.4 Kinematics in Oblique Coordinate Frames......Page 318
3.5 Curvilinear Coordinate System......Page 320
3.5.1 Principal and Reciprocal Base Vectors......Page 321
3.5.2 Principal–Reciprocal Transformation......Page 331
3.5.3 Curvilinear Geometry......Page 340
3.5.4 Curvilinear Kinematics......Page 345
3.5.5 Kinematics in Curvilinear Coordinates......Page 355
Key Symbols......Page 366
Exercises......Page 367
4.1 Rotation About Global Cartesian Axes......Page 377
4.2 Successive Rotations About Global Axes......Page 383
4.3 Global Roll–Pitch–Yaw Angles......Page 390
4.4 Rotation About Local Cartesian Axes......Page 393
4.5 Successive Rotations About Local Axes......Page 396
4.6 Euler Angles......Page 399
4.7 Local Roll–Pitch–Yaw Angles......Page 411
4.8 Local versus Global Rotation......Page 415
4.9 General Rotation......Page 417
4.10 Active and Passive Rotations......Page 429
4.11 Rotation of Rotated Body......Page 431
Key Symbols......Page 435
Exercises......Page 436
5.1 Axis–Angle Rotation......Page 442
5.2 Euler Parameters......Page 458
5.3 Quaternion......Page 469
5.4 Spinors and Rotators......Page 477
5.5 Problems in Representing Rotations......Page 479
5.5.1 Rotation Matrix......Page 480
5.5.2 Axis–Angle......Page 481
5.5.3 Euler Angles......Page 482
5.5.4 Quaternion and Euler Parameters......Page 483
5.6 Composition and Decomposition of Rotations......Page 485
5.6.1 Composition of Rotations......Page 486
5.6.2 Decomposition of Rotations......Page 488
Key Symbols......Page 490
Exercises......Page 491
6.1 Rigid-Body Motion......Page 497
6.2 Homogeneous Transformation......Page 501
6.3 Inverse and Reverse Homogeneous Transformation......Page 514
6.4 Compound Homogeneous Transformation......Page 520
6.5 Screw Motion......Page 537
6.6 Inverse Screw......Page 549
6.7 Compound Screw Transformation......Page 551
6.8 Plücker Line Coordinate......Page 554
6.9.1 Moment......Page 560
6.9.3 Plane and Line......Page 561
6.10 Screw and Pl¨ucker Coordinate......Page 565
Key Symbols......Page 567
Exercises......Page 568
7.1 Multibody Connection......Page 575
7.2 Denavit–Hartenberg Rule......Page 583
7.3 Forward Kinematics......Page 604
7.4 Assembling Kinematics......Page 635
7.5 Order-Free Rotation......Page 648
7.6 Order-Free Transformation......Page 655
7.7 Forward Kinematics by Screw......Page 663
7.8 Caster Theory in Vehicles......Page 669
7.9 Inverse Kinematics......Page 682
Key Symbols......Page 704
Exercises......Page 706
Part III Derivative Kinematics......Page 713
8.1 Angular Velocity......Page 715
8.2 Time Derivative and Coordinate Frames......Page 738
8.3 Multibody Velocity......Page 747
8.4 Velocity Transformation Matrix......Page 759
8.5 Derivative of a Homogeneous Transformation Matrix......Page 768
8.6 Multibody Velocity......Page 774
8.7 Forward-Velocity Kinematics......Page 777
8.8 Jacobian-Generating Vector......Page 785
8.9 Inverse-Velocity Kinematics......Page 798
Key Symbols......Page 802
Exercises......Page 803
9.1 Angular Acceleration......Page 808
9.2 Second Derivative and Coordinate Frames......Page 830
9.3 Multibody Acceleration......Page 843
9.4 Particle Acceleration......Page 850
9.5 Mixed Double Derivative......Page 878
9.6 Acceleration Transformation Matrix......Page 884
9.7 Forward-Acceleration Kinematics......Page 892
9.8 Inverse-Acceleration Kinematics......Page 894
Key Symbols......Page 897
Exercises......Page 898
10.1 Homogeneity and Isotropy......Page 907
10.2.1 Configuration Space......Page 910
10.2.2 Event Space......Page 916
10.2.3 State Space......Page 920
10.2.4 State–Time Space......Page 928
10.2.5 Kinematic Spaces......Page 930
10.3 Holonomic Constraint......Page 933
10.4 Generalized Coordinate......Page 943
10.5 Constraint Force......Page 952
10.6 Virtual and Actual Works......Page 955
10.7.1 Nonintegrable Constraint......Page 972
10.7.2 Inequality Constraint......Page 982
10.8 Differential Constraint......Page 986
10.9 Generalized Mechanics......Page 990
10.10 Integral of Motion......Page 996
10.11.1 Lagrange Method......Page 1016
10.11.2 Gauss Method......Page 1019
10.11.3 Hamilton Method......Page 1022
10.11.4 Gibbs–Appell Method......Page 1029
10.11.5 Kane Method......Page 1033
10.11.6 Nielsen Method......Page 1037
Key Symbols......Page 1041
Exercises......Page 1044
Part IV Dynamics......Page 1051
11.1 Rigid Body......Page 1053
11.2 Elements of the Mass Moment Matrix......Page 1055
11.3 Transformation of Mass Moment Matrix......Page 1064
11.4 Principal Mass Moments......Page 1078
Key Symbols......Page 1085
Exercises......Page 1086
12.1 Rigid-Body Rotational Cartesian Dynamics......Page 1092
12.2 Rigid-Body Rotational Eulerian Dynamics......Page 1116
12.3 Rigid-Body Translational Dynamics......Page 1121
12.4.1 Torque-Free Motion......Page 1132
12.4.2 Spherical Torque-Free Rigid Body......Page 1135
12.4.3 Axisymmetric Torque-Free Rigid Body......Page 1136
12.4.4 Asymmetric Torque-Free Rigid Body......Page 1148
12.4.5 General Motion......Page 1161
12.5 Multibody Dynamics......Page 1177
12.6 Recursive Multibody Dynamics......Page 1190
Key Symbols......Page 1197
Exercises......Page 1199
13.1 Lagrange Form of Newton Equations......Page 1209
13.2 Lagrange Equation and Potential Force......Page 1223
13.3 Variational Dynamics......Page 1235
13.4 Hamilton Principle......Page 1248
13.5 Lagrange Equation and Constraints......Page 1252
13.6 Conservation Laws......Page 1260
13.6.1 Conservation of Energy......Page 1261
13.6.2 Conservation of Momentum......Page 1263
13.7 Generalized Coordinate System......Page 1264
13.8 Multibody Lagrangian Dynamics......Page 1271
Key Symbols......Page 1282
Exercises......Page 1284
References......Page 1300
A Global Frame Triple Rotation......Page 1307
B Local Frame Triple Rotation......Page 1309
C Principal Central Screw Triple Combination......Page 1311
D Industrial Link DH Matrices......Page 1313
E Trigonometric Formula......Page 1320
Index......Page 1325

✦ Subjects

Транспорт;Авиационная техника;