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CHAPTER 1 Newton's Laws of Motion 3 1.1 Classical Mechanics 3 1.2 Space and Time 4 1.3 Mass and Force 9 1.4 Newton's First and Second Laws; Inertial Frames 13 1.5 The Third Law and Conservation of Momentum 17 1.6 Newton's Second Law in Cartesian Coordinates 23 1.7 Two-Dimensional Polar Coordinates 26 Principal Definitions and Equations of Chapter 1 33 Problems for Chapter 1 34 CHAPTER 2 Projectiles and Charged Particles 43 2.1 Air Resistance 43 2.2 Linear Air Resistance 46 2.3 Trajectory and Range in a Linear Medium 54 not covered 2.4 Quadratic Air Resistance 57 2.5 Motion of a Charge in a Uniform Magnetic Field 65 2.6 Complex Exponentials 68 2.7 Solution for the Charge in a B Field 70 Principal Definitions and Equations of Chapter 2 71 Problems for Chapter 2 72 CHAPTER 3 Momentum and Angular Momentum 83 3.1 Conservation of Momentum 83 3.2 Rockets 85 3.3 The Center of Mass 87 3.4 Angular Momentum for a Single Particle 90 3.5 Angular Momentum for Several Particles 93 Principal Definitions and Equations of Chapter 3 98 Problems for Chapter 3 99 CHAPTER 4 Energy 105 4.1 Kinetic Energy and Work 105 4.2 Potential Energy and Conservative Forces 109 4.3 Force as the Gradient of Potential Energy 116 4.4 The Second Condition that F be Conservative 118 4.5 Time-Dependent Potential Energy 121 4.6 Energy for Linear One-Dimensional Systems 123 4.7 Curvilinear One-Dimensional Systems 129 4.8 Central Forces 133 4.9 Energy of Interaction of Two Particles 138 4.10 The Energy of a Multiparticle System 144 Principal Definitions and Equations of Chapter 4 148 Problems for Chapter 4 150 CHAPTER 5 Oscillations 161 5.1 Hooke's Law 161 5.2 Simple Harmonic Motion 163 5.3 Two-Dimensional Oscillators 170 5.4 Damped Oscillations 173 5.5 Driven Damped Oscillations 179 5.6 Resonance 187 5.7 Fourier Series* 192 5.8 Fourier Series Solution for the Driven Oscillator* 197 5.9 The RMS Displacement; Parseval's Theorem' 203 Principal Definitions and Equations of Chapter 5 205 Problems for Chapter 5 207 CHAPTER 6 Calculus of Variations 215 6.1 Two Examples 216 6.2 The Euler-Lagrange Equation 218 6.3 Applications of the Euler-Lagrange Equation 221 6.4 More than Two Variables 226 Principal Definitions and Equations of Chapter 6 230 Problems for Chapter 6 230 CHAPTER 7 Lagrange's Equations 237 7.1 Lagrange's Equations for Unconstrained Motion 238 7.2 Constrained Systems; an Example 245 7.3 Constrained Systems in General 247 7.4 Proof of Lagrange's Equations with Constraints 250 7.5 Examples of Lagrange's Equations 254 7.6 Generalized Momenta and Ignorable Coordinates 266 7.7 Conclusion 267 7.8 More about Conservation Laws * 268 not covered 7.9 Lagrange's Equations for Magnetic Forces * 272 7.10 Lagrange Multipliers and Constraint Forces * 275 Principal Definitions and Equations of Chapter 7 280 Problems for Chapter 7 281 CHAPTER 8 Two-Body Central-Force Problems 293 8.1 The Problem 293 8.2 CM and Relative Coordinates; Reduced Mass 295 8.3 The Equations of Motion 297 8.4 The Equivalent One-Dimensional Problem 300 8.5 The Equation of the Orbit 305 8.6 The Kepler Orbits 308 8.7 The Unbounded Kepler Orbits 313 8.8 Changes of Orbit 315 Principal Definitions and Equations of Chapter 8 319 Problems for Chapter 8 320 CHAPTER 9 Mechanics in Noninertial Frames 327 9.1 Acceleration without Rotation 327 9.2 The Tides 330 9.3 The Angular Velocity Vector 336 9.4 Time Derivatives in a Rotating Frame 339 9.5 Newton's Second Law in a Rotating Frame 342 9.6 The Centrifugal Force 344 9.7 The Coriolis Force 348 9.8 Free Fall and the Coriolis Force 351 9.9 The Foucault Pendulum 354 9.10 Coriolis Force and Coriolis Acceleration 358 Principal Definitions and Equations of Chapter 9 359 Problems for Chapter 9 360

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