Classical Mechanics. Problems and Solutions

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Cover Half Title Title Page Copyright Page Dedication Table of Contents Preface Acknowledgments About the Authors Illustrations Julia R. D’Rozario Chapter 1: Newton’s Laws 1.1 Theory 1.1.1 Vectors 1.1.1.1 Space and Time 1.1.1.2 Position, Velocity, and Acceleration 1.1.1.3 Scalar (Dot) and Vector (Cross) Product 1.1.1.4 Gradient 1.1.1.5 Line Integral 1.1.1.6 Surface Integral 1.1.1.7 Volume Integral 1.1.1.8 Kronecker Delta 1.1.2 Coordinate Systems 1.1.2.1 Cartesian Coordinates 1.1.2.2 Cylindrical Polar Coordinates 1.1.2.3 Spherical Polar Coordinates 1.1.3 Newton’s Laws 1.1.3.1 Newton’s First Law – The Law of Inertia 1.1.3.2 Newton’s Second Law 1.1.3.3 Newton’s Third Law (Action–Reaction) 1.2 Problems and Solutions Chapter 2: Motion with Air Resistance 2.1 Theory 2.1.1 Drag Force of Air Resistance 2.2 Problems and Solutions Chapter 3: Momentum and Angular Momentum 3.1 Theory 3.1.1 Linear Momentum 3.1.2 Rockets 3.1.3 Center of Mass 3.1.4 Moment of Inertia 3.1.5 Principle of Conservation of Angular Momentum 3.1.6 Principle of Conservation of the Angular Momentum for a System of N Particles 3.2 Problems and Solutions Chapter 4: Energy 4.1 Theory 4.1.1 Work Kinetic Energy Theorem 4.1.2 Conservative Forces 4.1.3 Obtaining the Equation of the Motion from the Conservation of the Energy 4.2 Problems and Solutions Chapter 5: Oscillations 5.1 Theory 5.1.1 Hooke’s Law 5.1.2 Simple Harmonic Motion 5.1.3 Energy 5.1.4 Particular Types of Oscillations and the Differential Equations Associated with Them 5.1.4.1 Damped Oscillations 5.1.4.2 Weak Damping β ω0 5.1.4.5 Driven Damped Oscillations 5.2 Problems and Solutions Chapter 6: Lagrangian Formalism 6.1 Theory 6.1.1 The Lagrangian 6.1.2 Hamilton’s Principle 6.2 Problems and Solutions Chapter 7: Hamiltonian Formalism 7.1 Theory 7.1.1 The Hamiltonian 7.1.2 Example – One-Dimensional Systems 7.2 Problems and Solutions Chapter 8: Coupled Oscillators and Normal Modes 8.1 Theory 8.2 Problems and Solutions Chapter 9: Nonlinear Dynamics and Chaos 9.1 Theory 9.2 Problems and Solutions Chapter 10: Special Relativity 10.1 Theory 10.1.1 Galileo’s Transformations 10.1.2 Postulates of the Theory of Relativity 10.1.3 Lorentz Transformations 10.1.4 Length Contraction, Time Dilation 10.1.5 Composing Velocities 10.1.6 Relativistic Dynamics 10.1.7 Doppler Shift 10.1.7.1 Redshift 10.1.7.2 Blueshift 10.2 Problems and Solutions Appendix: Differential Equations Separable Equations First-Order Equations with an Integrating Factor Second-Order Homogeneous Equations Bibliography Index