| Preface |
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vii | |
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1 Fundamental Concepts And Laws Of Mechanics |
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1 | (2) |
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3 | (17) |
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1.1 Kinematics of a Moving Point: Displacement, Velocity and Acceleration |
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6 | (5) |
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8 | (3) |
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1.2 Moving Axes, Relative Velocity and Acceleration, Coriolis Acceleration |
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11 | (9) |
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2 Modelling of Material Bodies |
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20 | (1) |
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3 Newton's Laws of Motion: Force, Mass and Momentum |
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21 | (7) |
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23 | (5) |
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4 Units and Dimensions of Mechanical Quantities |
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28 | (2) |
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30 | (5) |
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31 | (4) |
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PART I ANALYTICAL STATICS |
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2 System Of Coplanar Forces Acting On A Body |
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35 | (1) |
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1 Two Forces Acting on a Particle |
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35 | (2) |
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2 n Coplanar Forces Acting on a Particle |
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37 | (6) |
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3 Two Forces Acting on a Body |
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43 | (4) |
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3.1 First Necessary Condition for Equilibrium |
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43 | (1) |
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3.2 Force Couple. Moment of a Force |
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44 | (1) |
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3.3 Second Necessary Condition for Equilibrium |
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45 | (1) |
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3.4 Sufficient Condition for Equilibrium: Rigid Bodies |
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46 | (1) |
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4 n Coplanar Forces Acting on a Body |
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47 | (17) |
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4.1 The Necessary Conditions for Equilibrium |
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47 | (1) |
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4.2 Equipollent Reduction of Forces |
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48 | (3) |
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4.3 Sufficient Conditions for Equilibrium: Rigid Bodies |
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51 | (12) |
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63 | (1) |
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64 | (4) |
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5.1 Equipollent Reduction |
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64 | (2) |
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66 | (2) |
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6 Application to Simple Truss Structures |
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68 | (4) |
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6.1 Truss Analysis: Methods of Joints and Sections |
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69 | (3) |
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72 | (23) |
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73 | (22) |
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95 | (1) |
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1 Equilibrium of a Particle Constrained on a Plane Curve |
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95 | (8) |
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2 Initial Motion on a Rough Surface: Tumbling, Rolling and Sliding |
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103 | (3) |
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3 Friction on rods in Continuous Contact with Planes |
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106 | (4) |
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110 | (2) |
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112 | (4) |
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116 | (11) |
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117 | (10) |
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127 | (2) |
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1 Plane Curvilinear Distribution |
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129 | (3) |
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132 | (4) |
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136 | (3) |
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139 | (3) |
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4.1 Theorems of Pappus and Guldinus |
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141 | (1) |
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5 Composite Plane Curves and Figures |
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142 | (4) |
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146 | (11) |
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146 | (11) |
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5 Equilibrium Of Flexible Strings |
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157 | (1) |
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1 Differential and Integral Equations for Equilibrium, Tangential Tension and Planar Form |
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157 | (3) |
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2 Uniform String: The Common Catenary |
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160 | (8) |
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3 Vertically Loaded String: The Parabolic Catenary |
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168 | (1) |
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4 Catenary of Uniform Strength |
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169 | (2) |
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5 String on Rough Curve: Belt Friction |
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171 | (2) |
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173 | (11) |
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173 | (11) |
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184 | (1) |
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1 Shear Force and Bending Moment |
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184 | (10) |
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185 | (3) |
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188 | (6) |
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2 Elasticity, Euler-Bernoulli Theory |
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194 | (12) |
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2.1 Clapeyron's Equation of Three Moments |
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201 | (5) |
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206 | (9) |
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207 | (8) |
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7 The Variational Principle Of Statics |
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215 | (1) |
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1 Real Displacement, Virtual Displacement and Virtual Work of a Force |
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215 | (1) |
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2 Lemma on Virtual Work of Forces of Constraints |
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216 | (2) |
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3 The Variational Principle of Virtual Work |
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218 | (1) |
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4 General Conditions for Equilibrium of n Coplanar Forces acting on a Rigid Body |
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219 | (1) |
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5 Application to the Common Catenary |
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220 | (1) |
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6 Application to the Elastic Beam Problem |
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221 | (2) |
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7 Simple Applications to Connected Bodies |
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223 | (9) |
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232 | (13) |
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233 | (12) |
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8 Stability Of Equilibrium |
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245 | (1) |
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1 Conservative Field of Forces and Potential Energy |
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245 | (4) |
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2 Equilibrium of a Material System under Conservative Field of Forces |
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249 | (1) |
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3 Conditions for Stability and Instability |
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249 | (3) |
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4 Criterion for Stability of a Heavy Rigid Body Resting on Top of a Rough Rigid Body |
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252 | (7) |
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259 | (11) |
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260 | (10) |
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9 System Of Forces In Three Dimensions |
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270 | (1) |
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1 n Forces Acting on a Particle |
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270 | (2) |
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2 n Forces Acting on a Body |
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272 | (21) |
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2.1 Equilibrium of a Body under Three, Four or Five Forces |
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279 | (14) |
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3 Parallel Forces, Centre of Gravity |
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293 | (1) |
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4 The Variational Principle and Stability Theory |
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294 | (4) |
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298 | (14) |
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298 | (14) |
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PART II ANALYTICAL DYNAMICS |
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10 Basic Equations Of Newtonian Dynamics Of Constant Mass |
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312 | (1) |
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1 Equations of Motion of a Particle and the Energy Integral |
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313 | (3) |
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2 Equations of Motion of a Body and the Momentum Equations |
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316 | (4) |
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2.1 Equations of Motion of the Centre of Mass and Motion about the Centre of Mass |
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317 | (2) |
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2.2 Energy and Momentum Integrals |
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319 | (1) |
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320 | (13) |
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3.1 Impulsive Motion of a Particle |
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321 | (1) |
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3.2 Impulsive Motion of a Body |
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322 | (1) |
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3.3 Kinetic Energy in Impulsive Motion: Carnot's Theorems |
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323 | (2) |
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3.4 Application to Elastic Impact of Smooth Spheres |
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325 | (8) |
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3.4.1 Impact of a smooth sphere with a plane |
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325 | (1) |
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3.4.2 Impact of two smooth spheres |
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326 | (7) |
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333 | (12) |
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334 | (11) |
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11 Rectilinear Motion Of A Particle |
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345 | (1) |
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1 Kinematics and Equations of Motion |
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345 | (2) |
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2 Motion Under Constant Force |
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347 | (1) |
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3 Variable Force: Integration of Equation of Motion |
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348 | (3) |
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4 Periodic Simple Harmonic Motion |
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351 | (10) |
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4.1 Motion of a Particle attached to a Horizontal Spring |
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355 | (3) |
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4.2 Motion of a Particle Suspended by a Vertical Spring |
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358 | (3) |
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5 Motion Under Inverse Square Law |
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361 | (2) |
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6 Vertical Motion in a Resisting Medium |
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363 | (7) |
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7 Damped Simple Harmonic Motion |
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370 | (2) |
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7.1 Damped, Forced Oscillations |
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371 | (1) |
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372 | (14) |
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372 | (14) |
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12 Motion In A Plane: Cartesian Coordinates |
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386 | (1) |
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1 Kinematics and Equations of Motion |
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386 | (3) |
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389 | (4) |
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3 Motion under Inverse Square Law |
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393 | (1) |
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4 Elliptic Harmonic Motion |
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394 | (5) |
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4.1 Differential Equation of the Path |
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397 | (2) |
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5 Motion of a Projectile in a Resisting Medium |
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399 | (5) |
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404 | (3) |
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407 | (11) |
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408 | (10) |
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13 Motion In A Plane: Polar Coordinates |
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418 | (1) |
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1 Kinematics, Equations of Motion |
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418 | (6) |
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1.1 Differential Equation of the Path |
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420 | (4) |
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2 Motion under Central Forces |
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424 | (10) |
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426 | (8) |
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3 Circular Orbit under any Central Force |
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434 | (2) |
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4 Motion under Inverse Square Law: Planetary Motion |
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436 | (10) |
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4.1 The Inverse Problem. Kepler's Laws |
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438 | (1) |
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4.2 Determination of Position |
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439 | (1) |
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440 | (6) |
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5 Perturbations in Planetary Orbits |
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446 | (4) |
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6 Application to Artificial Satellites and Ballistic Missiles |
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450 | (4) |
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454 | (12) |
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454 | (12) |
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14 Constrained Motion In A Plane |
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466 | (1) |
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1 Kinematics in Intrinsic Coordinates |
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466 | (2) |
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2 Motion of a Particle on a Plane Smooth Curve |
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468 | (13) |
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2.1 The Circular Pendulum |
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469 | (2) |
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2.2 Motion on a Smooth Vertical Circle |
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471 | (3) |
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2.3 Motion on a Smooth Cycloid: The Cycloidal Pendulum |
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474 | (2) |
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2.4 The Brachistochrone Problem |
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476 | (5) |
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3 Motion of a Particle on a Plane Rough Curve |
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481 | (4) |
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3.1 Motion on a Rough Cycloid |
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482 | (3) |
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485 | (11) |
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486 | (10) |
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15 Motion Of A Body Of Varying Mass |
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496 | (1) |
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1 Equation of Motion of a Body of Varying Mass |
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496 | (1) |
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497 | (5) |
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501 | (1) |
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502 | (2) |
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504 | (7) |
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504 | (7) |
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16 Motion Of A Rigid Body Parallel To A Plane And About A Fixed Point |
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511 | (1) |
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1 Moment of Inertia: Definitions |
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511 | (14) |
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513 | (4) |
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1.1.1 Principal Axes of Inertia |
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516 | (1) |
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1.2 Moments and Products of Inertia of Simple Bodies |
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517 | (8) |
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2 Motion of a Rigid Lamina Moving in its Own Plane |
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525 | (8) |
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3 Motion of a Symmetrical Body Moving Parallel to the Plane of Symmetry |
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533 | (6) |
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539 | (7) |
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5 Motion About a Fixed Point |
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546 | (6) |
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5.1 Steady Precession of a Spinning Top |
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548 | (1) |
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5.2 General Motion: Precession with Nutation |
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549 | (2) |
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551 | (1) |
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552 | (22) |
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552 | (22) |
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17 Impulsive Motion Of A Rigid Body Parallel To A Plane |
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574 | (1) |
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1 Impulsive Motion of a Rigid Plane Lamina Moving in its Own Plane |
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574 | (6) |
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2 Impulsive Motion of a Symmetrical Body Moving Parallel to the Plane of Symmetry |
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580 | (3) |
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2.1 The Ballistic Pendulum |
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582 | (1) |
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583 | (4) |
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587 | (9) |
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587 | (9) |
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18 Lagrange's And Hamilton's Equations Of Motion |
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596 | (1) |
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1 Dynamical Systems and Generalised Coordinates |
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596 | (2) |
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598 | (1) |
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599 | (8) |
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3.1 Application to a Simple Robotic Manipulator |
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605 | (2) |
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607 | (5) |
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4.1 Conservation Laws: Noether's Theorem |
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610 | (2) |
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5 Lagrange's Equations for Impulsive Motion |
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612 | (1) |
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613 | (3) |
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7 Hamilton-Jacobi Equation |
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616 | (3) |
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619 | (10) |
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620 | (9) |
| Bibliography |
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629 | (1) |
| Index |
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630 | |
