Advanced Engineering Dynamics
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Table of contents
- Cover
- Contentsvii
- Prefacexi
- Chapter 1. Newtonian Mechanics1
- 1.1 Introduction1
- 1.2 Fundamentals1
- 1.3 Space and time2
- 1.4 Mass3
- 1.5 Force5
- 1.6 Work and power5
- 1.7 Kinematics of a point6
- 1.8 Kinetics of a particle11
- 1.9 Impulse12
- 1.10 Kinetic energy13
- 1.11 Potential energy13
- 1.12 Coriolis’s theorem14
- 1.13 Newton’s laws for a group of particles15
- 1.14 Conservation of momentum17
- 1.15 Energy for a group of particles17
- 1.16 The principle of virtual work18
- 1.17 D’ Alembert’s principle19
- Chapter 2. Lagrange’s Equations21
- 2.1 Introduction21
- 2.2 Generalized co-ordinates23
- 2.3 Proof of Lagrange’s equations25
- 2.4 The dissipation function27
- 2.5 Kinetic energy29
- 2.6 Conservation laws31
- 2.7 Hamilton’s equations33
- 2.8 Rotating frame of reference and velocity-dependent potentials35
- 2.9 Moving co-ordinates39
- 2.10 Non-holonomic systems41
- 2.11 Lagrange’s equations for impulsive forces43
- Chapter 3. Hamilton's Principle46
- 3.1 Introduction46
- 3.2 Derivation of Hamilton's principle47
- 3.3 Application of Hamilton's principle49
- 3.4 Lagrange's equations derived from Hamilton's principle51
- 3.5 Illustrative example52
- Chapter 4. Rigid Body Motion in Three Dimensions55
- 4.1 Introduction55
- 4.2 Rotation55
- 4.3 Angular velocity58
- 4.4 Kinetics of a rigid body59
- 4.5 Moment of inertia61
- 4.6 Euler's equation for rigid body motion64
- 4.7 Kinetic energy of a rigid body65
- 4.8 Torque-free motion of a rigid body67
- 4.9 Stability of torque-free motion72
- 4.10 Euler's angles75
- 4.11 The symmetrical body76
- 4.12 Forced precession80
- 4.13 Epilogue83
- Chapter 5. Dynamics of Vehicles85
- 5.1 Introduction85
- 5.2 Gravitational potential85
- 5.3 The two-body problem88
- 5.4 The central force problem90
- 5.5 Satellite motion93
- 5.6 Effects of oblateness100
- 5.7 Rocket in free space103
- 5.8 Non-spherical satellite106
- 5.9 Spinning satellite107
- 5.10 De-spinning of satellites107
- 5.11 Stability of aircraft109
- 5.12 Stability of a road vehicle118
- Chapter 6. Impact and One-Dimensional Wave Propagation125
- 6.1 Introduction125
- 6.2 The one-dimensional wave125
- 6.3 Longitudinal waves in an elastic prismatic bar128
- 6.4 Reflection and transmission at a boundary130
- 6.5 Momentum and energy in a pulse132
- 6.6 Impact of two bars133
- 6.7 Constant force applied to a long bar136
- 6.8 The effect of local deformation on pulse shape138
- 6.9 Prediction of pulse shape during impact of two bars141
- 6.10 Impact of a rigid mass on an elastic bar145
- 6.11 Dispersive waves149
- 6.12 Waves in a uniform beam155
- 6.13 Waves in periodic structures161
- 6.14 Waves in a helical spring163
- Chapter 7. Waves in a Three-Dimensional Elastic Solid172
- 7.1 Introduction172
- 7.2 Strain172
- 7.3 Stress176
- 7.4 Elastic constants177
- 7.5 Equations of motion178
- 7.6 Wave equation for an elastic solid179
- 7.7 Plane strain184
- 7.8 Reflection at a plane surface186
- 7.9 Surface waves (Rayleigh waves)189
- 7.10 Conclusion192
- Chapter 8. Robot Arm Dynamics194
- 8.1 Introduction194
- 8.2 Typical arrangements194
- 8.3 Kinematics of robot arms197
- 8.4 Kinetics of a robot arm223
- Chapter 9. Relativity235
- 9.1 Introduction235
- 9.2 The foundations of the special theory of relativity235
- 9.3 Time dilation and proper time240
- 9.4 Simultaneity241
- 9.5 The Doppler effect242
- 9.6 Velocity246
- 9.7 The twin paradox249
- 9.8 Conservation of momentum250
- 9.9 Relativistic force252
- 9.10 Impact of two particles254
- 9.11 The relativistic Lagrangian256
- 9.12 Conclusion258
- Problems261
- Appendix 1 - Vectors, Tensors and Matrices272
- Appendix 2 - Analytical Dynamics281
- Appendix 3 - Curvilinear Co-ordinate Systems288
- Bibliography297
- Index299
'Advanced Engineering Dynamics' bridges the gap between elementary dynamics and advanced specialist applications in engineering.
It begins with a reappraisal of Newtonian principles before expanding into analytical dynamics typified by the methods of Lagrange and by Hamilton's Principle and rigid body dynamics. Four distinct vehicle types (satellites, rockets, aircraft and cars) are examined highlighting different aspects of dynamics in each case. Emphasis is placed on impact and one dimensional wave propagation before extending the study into three dimensions. Robotics is then looked at in detail, forging a link between conventional dynamics and the highly specialised and distinctive approach used in robotics. The text finishes with an excursion into the Special Theory of Relativity mainly to define the boundaries of Newtonian Dynamics but also to re-appraise the fundamental definitions. Through its examination of specialist applications highlighting the many different aspects of dynamics this text provides an excellent insight into advanced systems without restricting itself to a particular discipline. The result is essential reading for all those requiring a general understanding of the more advanced aspects of engineering dynamics.
It begins with a reappraisal of Newtonian principles before expanding into analytical dynamics typified by the methods of Lagrange and by Hamilton's Principle and rigid body dynamics. Four distinct vehicle types (satellites, rockets, aircraft and cars) are examined highlighting different aspects of dynamics in each case. Emphasis is placed on impact and one dimensional wave propagation before extending the study into three dimensions. Robotics is then looked at in detail, forging a link between conventional dynamics and the highly specialised and distinctive approach used in robotics. The text finishes with an excursion into the Special Theory of Relativity mainly to define the boundaries of Newtonian Dynamics but also to re-appraise the fundamental definitions. Through its examination of specialist applications highlighting the many different aspects of dynamics this text provides an excellent insight into advanced systems without restricting itself to a particular discipline. The result is essential reading for all those requiring a general understanding of the more advanced aspects of engineering dynamics.