This book of problems and solutions in classical mechanics is dedicated to junior or senior undergraduate students in physics, engineering, applied mathematics, astronomy, or chemistry who may want to improve their problems solving skills, or to freshman graduate students who may be seeking a refresh of the material.
The book is structured in ten chapters, starting with Newton’s laws, motion with air resistance, conservation laws, oscillations, and the Lagrangian and Hamiltonian Formalisms. The last two chapters introduce some ideas in nonlinear dynamics, chaos, and special relativity. Each chapter starts with a brief theoretical outline, and continues with problems and detailed solutions. A concise presentation of differential equations can be found in the appendix. A variety of problems are presented, from the standard classical mechanics problems, to context-rich problems and more challenging problems.
Key features:
- Presents a theoretical outline for each chapter.
- Motivates the students with standard mechanics problems with step-by-step explanations.
- Challenges the students with more complex problems with detailed solutions.
Author(s): Elina M. van Kempen, Carolina C. Ilie, Zachariah S. Schrecengost
Edition: 1
Publisher: CRC Press
Year: 2022
Language: English
Pages: 264
City: Boca Raton
Tags: Classical Mechanics; Physics; Engineering; Applied Mathematics; Astronomy; Newton's Laws; Motion; Air Resistance; Conservation Laws; Oscillations; Lagrangian Formalisms; Hamiltonian Formalisms; Nonlinear Dynamics; Chaos; Special Relativity
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
