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xiii | |
Preface |
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xxiii | |
Acknowledgement |
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xxvii | |
Introduction |
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xxix | |
About the Companion Website |
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xliii | |
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1 Kinematics of Particles |
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1 | (26) |
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1 | (1) |
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2 | (2) |
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4 | (4) |
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1.4 Velocity of a Particle in a Three-dimensional Space |
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8 | (6) |
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1.5 Acceleration of a Particle in a Three-dimensional Space |
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14 | (13) |
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21 | (6) |
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2 Dynamics of Particles: Vectorial Approach |
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27 | (28) |
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2.1 Newton's Second Law of Dynamics |
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27 | (10) |
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2.2 Stiffness and Viscous Damping |
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37 | (3) |
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40 | (3) |
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2.4 Dynamics of a System of Particles |
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43 | (4) |
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2.5 Newton's Law of Gravitation |
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47 | (8) |
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50 | (4) |
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54 | (1) |
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3 Dynamics of Rigid Bodies: Vectorial Approach |
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55 | (48) |
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55 | (2) |
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3.2 Mass Moment of Inertia |
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57 | (4) |
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3.3 Parallel Axis Theorem |
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61 | (4) |
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3.4 Rotation of the Inertia Matrix |
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65 | (4) |
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66 | (3) |
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3.5 Planar Motion of Rigid Bodies |
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69 | (14) |
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3.5.1 Moment about an Inertial Point |
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72 | (1) |
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3.5.2 Moment about a Moving Point on the Body |
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73 | (1) |
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3.5.3 Moment about the Center of Mass or a Fixed Point on the Body |
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73 | (10) |
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3.6 Non-planar Rigid-body Motion |
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83 | (20) |
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3.6.1 Euler Rotational Equations |
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85 | (9) |
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94 | (7) |
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101 | (2) |
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4 System Constraints and Virtual Displacement |
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103 | (14) |
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103 | (7) |
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4.1.1 Classification of Constraints |
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104 | (6) |
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4.2 Actual and Virtual Displacements |
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110 | (3) |
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113 | (4) |
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115 | (1) |
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116 | (1) |
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5 Dynamics of Particles: Analytical Approach |
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117 | (44) |
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5.1 The Brachistochrone Problem |
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117 | (6) |
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5.2 Lagrange's Equation for a Conservative System |
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123 | (8) |
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5.3 Lagrange's Equation for Non-conservative Systems |
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131 | (10) |
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134 | (7) |
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5.4 Lagrange's Equations with Constraints |
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141 | (10) |
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5.4.1 Physical Interpretation of Lagrange Multipliers |
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146 | (5) |
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151 | (3) |
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5.6 Advantages and Disadvantages of the Analytical Approach |
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154 | (7) |
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155 | (4) |
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159 | (2) |
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6 Dynamics of Rigid Bodies: Analytical Approach |
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161 | (22) |
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6.1 Kinetic Energy of a Rigid Body |
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161 | (5) |
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6.2 Lagrange's Equation Applied to Rigid Bodies |
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166 | (17) |
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176 | (7) |
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183 | (44) |
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183 | (3) |
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186 | (6) |
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7.3 Angular Momentum of Particles |
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192 | (7) |
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195 | (4) |
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7.4 Angular Momentum of Rigid Bodies (Planar Motion) |
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199 | (6) |
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7.4.1 Angular Momentum about an Axis Passing through the Center of Mass |
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199 | (2) |
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7.4.2 Angular Momentum about an Axis Passing through a Fixed Point on the Body |
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201 | (1) |
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7.4.3 Angular Momentum about an Axis Passing through an Arbitrary Inertial Point |
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201 | (4) |
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7.5 Angular Momentum of Rigid Bodies (Non-planar Motion) |
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205 | (8) |
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7.5.1 Angular Momentum about a Set of Axes Located at the Center of Mass |
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205 | (1) |
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7.5.2 Angular Momentum about a Set of Axes Located at a Fixed Point |
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206 | (1) |
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7.5.3 Angular Momentum about a Set of Axes Located at an Arbitrary Inertial Point |
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206 | (1) |
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7.5.4 Conservation of Angular Momentum for Rigid Bodies |
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206 | (7) |
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213 | (14) |
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219 | (8) |
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8 Motion of Charged Bodies in an Electric Field |
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227 | (58) |
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227 | (20) |
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8.1.1 Electrostatic Forces |
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227 | (2) |
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229 | (3) |
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232 | (2) |
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8.1.4 Electrostatic Potential Energy |
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234 | (1) |
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8.1.5 Electric Potential (Voltage) |
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235 | (2) |
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237 | (2) |
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8.1.7 Motion in an Electric Field |
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239 | (8) |
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247 | (21) |
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8.2.1 Electromagnetic Force |
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247 | (6) |
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8.2.2 Forces on a Current-carrying Conductor |
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253 | (2) |
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8.2.3 Electromagnetic Coupling |
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255 | (2) |
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257 | (5) |
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8.2.5 Faraday's Law of Induction |
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262 | (6) |
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8.3 Lagrangian Formulation for Electrical Elements |
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268 | (5) |
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268 | (1) |
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269 | (1) |
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269 | (4) |
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273 | (2) |
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8.4.1 Maxwell's First Equation |
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273 | (1) |
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8.4.2 Maxwell's Second Equation |
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273 | (1) |
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8.4.3 Maxwell's Third Equation |
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274 | (1) |
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8.4.4 Maxwell's Fourth Equation |
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274 | (1) |
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8.5 Lagrangian Formulation of the Lorentz Force |
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275 | (10) |
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279 | (5) |
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284 | (1) |
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9 Introduction to Analysis Tools |
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285 | (42) |
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285 | (2) |
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9.2 Equilibrium Solutions of Dynamical Systems |
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287 | (1) |
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9.3 Stability and Classification of Equilibrium Solutions |
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288 | (8) |
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9.4 Phase-plane Representation of the Dynamics |
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296 | (12) |
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9.4.1 Conservative Systems |
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296 | (7) |
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9.4.2 Non-conservative Systems |
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303 | (5) |
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9.5 Bifurcation of Equilibrium Solutions |
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308 | (15) |
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9.5.1 Static Bifurcations |
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308 | (7) |
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9.5.2 Dynamic (Hopf) Bifurcation |
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315 | (8) |
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323 | (4) |
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324 | (2) |
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326 | (1) |
Index |
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327 | |