AHMED A. SHABANA is University Distinguished Professor and the Richard and Loan Hill Professor of Engineering at the University of Illinois at Chicago, United States. He is a Fellow of the American Society of Mechanical Engineers (ASME), a Fellow of the Society of Automotive Engineering (SAE International), and the author of texts in the areas of dynamics and vibration.

Preface ix
1 Introduction 1
1.1 Differential Geometry 4
1.2 Integration of Geometry and Mechanics 9
1.3 Hunting Oscillations 14
1.4 Wheel and Track Geometries 17
1.5 Centrifugal Forces and Balance Speed 22
1.6 Contact Formulations 26
1.7 Computational MBS Approaches 28
1.8 Derailment Criteria 33
1.9 High-Speed Rail Systems 36
1.10 Linear Algebra and Book Notations 41
2 Differential Geometry 45
2.1 Curve Geometry 46
2.2 Surface Geometry 54
2.3 Application to Railroad Geometry 57
2.4 Surface Tangent Plane and Normal Vector 60
2.5 Surface Fundamental Forms 62
2.6 Normal Curvature 69
2.7 Principal Curvatures and Directions 72
2.8 Numerical Representation of the Profile Geometry 76
2.9 Numerical Representation of Surface Geometry 78
3 Motion and Geometry Descriptions 83
3.1 Rigid-Body Kinematics 84
3.2 Direction Cosines and Simple Rotations 86
3.3 Euler Angles 88
3.4 Euler Parameters 91
3.5 Velocity and Acceleration Equations 95
3.6 Generalized Coordinates 97
3.7 Kinematic Singularities 100
3.8 Euler Angles and Track Geometry 102
3.9 Angle Representation of the Curve Geometry 107
3.10 Euler Angles as Field Variables 108
3.11 Euler-Angle Description of the Track Geometry 111
3.12 Geometric Motion Constraints 114
3.13 Trajectory Coordinates 119
4 Railroad Geometry 125
4.1 Wheel Surface Geometry 126
4.2 Wheel Curvatures and Global Vectors 132
4.3 Semi-analytical Approach for Rail Geometry 135
4.4 ANCF Rail Geometry 142
4.5 ANCF Interpolation of Rail Geometry 145
4.6 ANCF Computation of Tangents and Normal 146
4.7 Track Geometry Equations 148
4.8 Numerical Representation of Track Geometry 152
4.9 Track Data 155
4.10 Irregularities and Measured Track Data 162
4.11 Comparison of the Semi-Analytical and ANCF Approaches 169
5 Contact Problem 175
5.1 Wheel/Rail Contact Mechanism 177
5.2 Constraint Contact Formulation (CCF) 183
5.3 Elastic Contact Formulation (ECF) 184
5.4 Normal Contact Forces 187
5.5 Contact Surface Geometry 188
5.6 Contact Ellipse and Normal Contact Force 194
5.7 Creepage Definitions 199
5.8 Creep Force Formulations 203
5.9 Creep Force and Wheel/Rail Contact Formulations 213
5.10 Maglev Forces 219
6 Equations of Motion 225
6.1 Newtonian and Lagrangian Approaches 226
6.2 Virtual Work Principle and Constrained Dynamics 227
6.3 Summary of Rigid-Body Kinematics 232
6.4 Inertia Forces 235
6.5 Applied Forces 239
6.6 Newton-Euler Equations 241
6.7 Augmented Formulation and Embedding Technique 244
6.8 Wheel/Rail Constraint Contact Forces 254
6.9 Wheel/Rail Elastic Contact Forces 259
6.10 Other Force Elements 261
6.11 Trajectory Coordinates 268
6.12 Longitudinal Train Dynamics (LTD) 274
6.13 Hunting Stability 280
6.14 MBS Modeling of Electromechanical Systems 288
7 Pantograph/Catenary Systems 291
7.1 Pantograph/Catenary Design 292
7.2 ANCF Catenary Kinematic Equations 298
7.3 Catenary Inertia and Elastic Forces 304
7.4 Catenary Equations of Motion 306
7.5 Pantograph/Catenary Contact Frame 308
7.6 Constraint Contact Formulation (CCF) 310
7.7 Elastic Contact Formulation (ECF) 314
7.8 Pantograph/Catenary Equations and MBS Algorithms 317
7.9 Pantograph/Catenary Contact Force Control 321
7.10 Aerodynamic Forces 322
7.11 Pantograph/Catenary Wear 324
Appendix Contact Equations and Elliptical Integrals 329
A.1 Derivation of the Contact Equations 329
A.2 Elliptical Integrals 332
Bibliography 335
Index 355