| Preface |
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xii | |
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1 | (78) |
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1.1 Fundamental Assumptions Underlying Newtonian Dynamics |
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1 | (2) |
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1.2 Galilean and Non-Galilean Reference Frames |
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3 | (3) |
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1.3 Dynamics of a Free Particle: Newton's First Law (Principle of Inertia) |
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6 | (1) |
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1.4 Dynamics of Interacting Particles |
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7 | (4) |
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1.5 Closing the Formulation of Dynamics: From Mach's Axiomalics to Newton's Laws, and Principle of Determinacy |
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11 | (1) |
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1.6 Usual Galilean Reference Frames |
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12 | (1) |
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1.7 Interaction Forces between Particles: Kinematic Dependency |
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13 | (2) |
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1.8 Contact Forces between Particles and Extended Bodies |
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15 | (1) |
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1.9 Formulation of Interaction Forces |
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16 | (6) |
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1.10 Characterization and Limit Conditions of Constraint Forces: Friction Forces |
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22 | (6) |
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1.11 Dynamics in Non-Galilean Reference Frames: Inertial Forces |
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28 | (3) |
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31 | (48) |
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Appendix 1A Gravitational Field Outside and Inside the Earth's Surface |
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36 | (3) |
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Appendix 1B Dynamics in the Terrestrial Reference Frame (TRF) |
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39 | (3) |
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42 | (19) |
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61 | (8) |
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69 | (3) |
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72 | (1) |
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72 | (3) |
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75 | (4) |
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2 Interaction Forces between Rigid Bodies |
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79 | (72) |
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2.1 Torsor of a System of Forces |
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80 | (2) |
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2.2 Formulation of Interaction Torsors: Gravitational Torsor, and Torsion Springs, Dampers, and Drivers |
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82 | (3) |
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2.3 Constraint Torsor between Two Rigid Bodies: Indeterminacy and Ill-Conditioning |
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85 | (9) |
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2.4 Constraint Torsors between Rigid Bodies: Analytical Characterization |
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94 | (7) |
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2.5 Constraint Auxiliary Elements |
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101 | (8) |
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2.6 Constraints in Multibody Systems: Indeterminacy and Ill-Conditioning |
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109 | (8) |
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2.7 Limit Conditions in Multiple-Point Unilateral Constraints: Contact Loss and Overturning |
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117 | (3) |
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2.8 Additional Limit Conditions: Sliding, Rolling, and Pivoting |
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120 | (31) |
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Appendix 2A Gravitational Moments |
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124 | (2) |
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126 | (19) |
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145 | (2) |
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147 | (1) |
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147 | (4) |
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151 | (51) |
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151 | (2) |
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3.2 Analytical Calculation of the Center of Mass: Pappus-Guldin Theorems |
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153 | (5) |
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158 | (4) |
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162 | (4) |
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166 | (1) |
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3.6 Principal Directions of Inertia: Symmetrical and Spherical Rotors |
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167 | (7) |
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3.7 Practical Tips to Calculate the Inertia Tensor about a Point Q |
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174 | (5) |
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179 | (23) |
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183 | (13) |
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196 | (4) |
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200 | (1) |
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200 | (2) |
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202 | (114) |
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4.1 Linear Momentum Theorem in Galilean Reference Frames |
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203 | (3) |
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4.2 Angular Momentum Theorem in Galilean Reference Frames |
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206 | (6) |
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4.3 Barycentric Decomposition of the Angular Momentum |
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212 | (2) |
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4.4 Angular Momentum of a Rigid Body |
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214 | (13) |
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4.5 Dynamic Properties of the Principal Axes of Inertia (PAI) |
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227 | (7) |
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4.6 Time Integral of the Vector Theorems: Force Impulse and Angular Impulse |
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234 | (4) |
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4.7 Vector Theorems in General Non-Galilean Reference Frames |
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238 | (78) |
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Appendix 4A Static and Dynamic Balancing of a Rotor |
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244 | (4) |
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248 | (28) |
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276 | (26) |
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302 | (3) |
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305 | (1) |
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305 | (7) |
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312 | (4) |
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316 | (90) |
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5.1 Work-Energy Theorem: Kinetic Energy, Work and Power done by a Force |
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317 | (2) |
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5.2 Barycentric Decomposition of the Kinetic Energy |
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319 | (1) |
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5.3 Work-Energy Theorem in Non-Galilean Reference Frames with Translational Motion Relative to a Galilean Frame |
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320 | (2) |
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5.4 Kinetic Energy of a Rigid Body |
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322 | (5) |
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5.5 Work Associated with the Internal Forces |
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327 | (6) |
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5.6 Work Associated with the Forces on a Rigid Body |
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333 | (1) |
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5.7 Work Associated with External Constraint and Friction Forces |
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334 | (2) |
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5.8 Work Associated with Conservative Forces: Conservative Systems |
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336 | (2) |
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338 | (6) |
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5.10 One-DoF Systems with Constant Mechanical Energy: Equilibrium Configurations and Stability |
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344 | (4) |
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5.11 The Utopia of Perpetual Motion |
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348 | (5) |
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5.12 Work-Energy Theorem in Non-Galilean Reference Frames |
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353 | (53) |
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Appendix 5A Rotation Stability in a Free Rigid Body |
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357 | (4) |
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361 | (22) |
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383 | (15) |
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398 | (2) |
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400 | (1) |
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400 | (4) |
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404 | (2) |
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6 The Method of Virtual Power |
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406 | (57) |
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6.1 D'Alembert Inertial Forces: Formulation of the Method of Virtual Power |
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406 | (2) |
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6.2 The Equations of Motion through the MVP |
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408 | (3) |
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6.3 The Constraint Forces through the MVP |
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411 | (3) |
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6.4 Torsor of D'Alembert Inertial Forces in a Rigid Body |
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414 | (49) |
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425 | (15) |
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440 | (14) |
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454 | (2) |
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456 | (1) |
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456 | (4) |
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460 | (3) |
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463 | (41) |
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7.1 Generalized Forces in the Method of Virtual Power |
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463 | (1) |
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7.2 Components of the Generalized D'Alembert Inertial Force |
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464 | (3) |
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7.3 Components of the Generalized Conservative Force |
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467 | (1) |
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468 | (4) |
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7.5 Constraint Forces from Lagrange's Equations |
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472 | (2) |
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7.6 Lagrange's Equations with Multipliers |
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474 | (4) |
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478 | (26) |
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Appendix 7A Equilibrium Configurations |
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479 | (3) |
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482 | (12) |
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494 | (8) |
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502 | (1) |
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502 | (2) |
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8 Introduction to Percussive Dynamics |
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504 | (75) |
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8.1 Introduction to Percussive Problems |
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504 | (6) |
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8.2 Percussive Behavior of Constraints |
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510 | (4) |
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8.3 Percussions Associated with Dry Friction |
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514 | (1) |
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8.4 Percussive Formulation of the Vector Theorems |
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515 | (4) |
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519 | (1) |
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8.6 Percussive Formulation of the Work-Energy Theorem |
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520 | (3) |
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8.7 Energy Balance: Newton's Restitution Rule |
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523 | (8) |
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8.8 Percussive Formulation of the Method of Virtual Power |
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531 | (2) |
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8.9 Percussive Formulation of Lagrange's Equations |
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533 | (4) |
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8.10 Multiple-Point Collisions |
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537 | (42) |
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Appendix 8A Rough Collisions |
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540 | (4) |
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544 | (19) |
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563 | (11) |
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574 | (1) |
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575 | (1) |
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575 | (2) |
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577 | (2) |
| Bibliography |
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579 | (1) |
| Further Reading |
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579 | (1) |
| Index |
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