Classical Mechanics: Problems and Solutions

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
			5.1.4.3 Critical Damping β = ω0
			5.1.4.4 Strong 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