Preface

• Purpose of This Book (trial)
• Approach and Philosophy (trial)
• Mathematical Requirements (trial)
• Importance of Classical Mechanics
• How to Use This Book (trial)
• Final Note (trial)

Introduction to Mechanics

• What is Mechanics? (trial)
• Importance of Mechanics (trial)
• Branches of Mechanics (trial)
• Idealizations in Mechanics (trial)
• Space and Time (trial)
• Reference Frames (trial)
• Physical Quantities and Units (trial)
• Dimensions (trial)
• Dimensional Analysis (trial)
• Mathematical Description of Motion (trial)
• Visualization of Motion (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Mathematical Foundations of Mechanics

• Introduction (trial)
• Scalars and Vectors (trial)
• Representation of Vectors (trial)
• Vector Addition (trial)
• Dot Product (Scalar Product) (trial)
• Cross Product (Vector Product) (trial)
• Unit Vectors (trial)
• Direction Cosines (trial)
• Differentiation of Vectors (trial)
• Units and Dimensions (trial)
• Dimensional Analysis (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Kinematics of Particles

• Introduction (trial)
• Position of a Particle (trial)
• Displacement (trial)
• Velocity (trial)
• Acceleration (trial)
• Motion with Constant Acceleration (trial)
• Derivation of Equations of Motion (trial)
• Graphical Representation of Motion (trial)
• Projectile Motion (trial)
• Important Results in Projectile Motion (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Newton’s Laws of Motion

• Introduction (trial)
• Concept of Force (trial)
• Types of Forces (trial)
• Newton’s First Law (trial)
• Newton’s Second Law (trial)
• Newton’s Third Law (trial)
• Free Body Diagrams (FBD) (trial)
• Friction (trial)
• Tension (trial)
• Motion on a Horizontal Surface (trial)
• Motion on an Inclined Plane (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Work and Energy

• Introduction (trial)
• Work (trial)
• Special Cases of Work (trial)
• Work-Energy Theorem (trial)
• Potential Energy (trial)
• Conservative and Non-Conservative Forces (trial)
• Conservation of Mechanical Energy (trial)
• Power (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Systems of Particles and Linear Momentum

• Introduction (trial)
• Linear Momentum (trial)
• Newton’s Second Law in Momentum Form (trial)
• Impulse (trial)
• System of Particles (trial)
• Total Momentum of a System (trial)
• Center of Mass (trial)
• Motion of Center of Mass (trial)
• Conservation of Linear Momentum (trial)
• Collisions (trial)
• Types of Collisions (trial)
• One-Dimensional Collision (trial)
• Coefficient of Restitution (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Rotational Motion and Angular Momentum

• Introduction (trial)
• Angular Variables (trial)
• Relation Between Linear and Angular Quantities (trial)
• Rotational Kinematics (trial)
• Torque (trial)
• Moment of Inertia (trial)
• Newton’s Second Law for Rotation (trial)
• Angular Momentum (trial)
• Conservation of Angular Momentum (trial)
• Rotational Kinetic Energy (trial)
• Rolling Motion (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Gravitation

• Introduction (trial)
• Newton’s Law of Universal Gravitation (trial)
• Gravitational Field (trial)
• Acceleration Due to Gravity (trial)
• Variation of Gravity (trial)
• Gravitational Potential Energy (trial)
• Gravitational Potential (trial)
• Escape Velocity (trial)
• Orbital Motion (trial)
• Kepler’s Laws of Planetary Motion (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Oscillations

• Introduction (trial)
• Periodic Motion (trial)
• Simple Harmonic Motion (SHM) (trial)
• Solution of SHM (trial)
• Velocity and Acceleration (trial)
• Key Features of SHM (trial)
• Energy in SHM (trial)
• Graphical Representation (trial)
• Mass-Spring System (trial)
• Simple Pendulum (trial)
• Damped Oscillations (trial)
• Forced Oscillations and Resonance (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Non-Inertial Frames

• Introduction (trial)
• Inertial vs Non-Inertial Frames (trial)
• Need for Fictitious Forces (trial)
• Fictitious Force in Linear Acceleration (trial)
• Example: Accelerating Elevator (trial)
• Rotating Frames (trial)
• Centrifugal Force (trial)
• Coriolis Force (trial)
• Motion in Rotating Frame (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Lagrangian Mechanics

• Introduction (trial)
• Generalized Coordinates (trial)
• Degrees of Freedom (trial)
• Constraints (trial)
• The Lagrangian (trial)
• Principle of Least Action (trial)
• Euler-Lagrange Equation (trial)
• Physical Meaning (trial)
• Example: Free Particle (trial)
• Example: Simple Harmonic Oscillator (trial)
• Example: Simple Pendulum (trial)
• Small Angle Approximation (trial)
• Advantages of Lagrangian Mechanics (trial)
• Conserved Quantities (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Hamiltonian Mechanics

• Introduction (trial)
• Generalized Coordinates and Momenta (trial)
• The Hamiltonian (trial)
• Hamilton’s Equations of Motion (trial)
• Physical Meaning (trial)
• Phase Space (trial)
• Example: Free Particle (trial)
• Example: Simple Harmonic Oscillator (trial)
• Conservation of Energy (trial)
• Canonical Variables (trial)
• Advantages of Hamiltonian Mechanics (trial)
• Hamiltonian for Multiple Particles (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Central Force Motion

• Introduction (trial)
• Definition of Central Force (trial)
• Properties of Central Forces (trial)
• Torque in Central Force (trial)
• Conservation of Angular Momentum (trial)
• Motion in Plane Polar Coordinates (trial)
• Equation of Motion (trial)
• Conservation of Angular Momentum (trial)
• Effective Potential (trial)
• Total Energy (trial)
• Orbital Equation (trial)
• Inverse Square Law Force (trial)
• Kepler’s Laws Revisited (trial)
• Circular Orbits (trial)
• Stability of Circular Orbits (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Rigid Body Dynamics

• Introduction (trial)
• Types of Motion of a Rigid Body (trial)
• Center of Mass Motion (trial)
• Rotation About a Fixed Axis (trial)
• Angular Momentum of Rigid Body (trial)
• Kinetic Energy of Rigid Body (trial)
• Parallel Axis Theorem (trial)
• Perpendicular Axis Theorem (trial)
• Rolling Motion (trial)
• Energy in Rolling Motion (trial)
• Angular Momentum About Different Points (trial)
• Equilibrium of Rigid Body (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Small Oscillations and Normal Modes

• Introduction (trial)
• Equilibrium and Stability (trial)
• Small Oscillations Approximation (trial)
• Equation of Motion (trial)
• Frequency of Small Oscillations (trial)
• Systems with Two Degrees of Freedom (trial)
• Coupled Oscillations (trial)
• Normal Modes (trial)
• Solving for Normal Modes (trial)
• Example: Two Coupled Masses (trial)
• Matrix Formulation (trial)
• Eigenvalue Problem (trial)
• Energy in Coupled Systems (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Introduction to Nonlinear Dynamics and Chaos

• Introduction (trial)
• Linear vs Nonlinear Systems (trial)
• Characteristics of Nonlinear Systems (trial)
• Phase Space Representation (trial)
• Fixed Points (Equilibrium Points) (trial)
• Stability Analysis (trial)
• Example: Nonlinear Oscillator (trial)
• Chaos (trial)
• Sensitive Dependence (trial)
• Example: Double Pendulum (trial)
• Strange Attractors (trial)
• Logistic Map (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Variational Principles and Applications

• Introduction (trial)
• The Concept of Action (trial)
• Principle of Stationary Action (trial)
• Variation of a Function (trial)
• Derivation of Euler-Lagrange Equation (trial)
• Euler-Lagrange Equation (trial)
• Physical Interpretation (trial)
• Example: Free Particle (trial)
• Example: Harmonic Oscillator (trial)
• Example: Motion in Gravitational Field (trial)
• Generalized Coordinates (trial)
• Cyclic Coordinates (trial)
• Noether’s Theorem (Introductory Idea) (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Appendix: Mathematical Methods for Mechanics

• Introduction (trial)
• Functions and Graphs (trial)
• Limits (trial)
• Derivatives (trial)
• Physical Interpretation (trial)
• Integrals (trial)
• Vector Algebra (trial)
• Coordinate Systems (trial)
• Differential Equations (trial)
• Series Expansion (trial)
• Dimensional Analysis (trial)
• Trigonometric Identities (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Appendix: Problem-Solving Techniques in Mechanics

• Introduction (trial)
• General Strategy for Problem Solving (trial)
• Choosing the Right Method (trial)
• Free Body Diagrams (FBD) (trial)
• Common Mistakes (trial)
• Dimensional Checking (trial)
• Estimation Techniques (trial)
• Problem Types (trial)
• Worked Example (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Appendix: Units, Constants, and Reference Data

• Introduction (trial)
• SI System of Units (trial)
• Important Physical Constants (trial)
• Prefixes (trial)
• Unit Conversions (trial)
• Dimensional Formulae (trial)
• Useful Mathematical Constants (trial)
• Approximation Values (trial)
• Scientific Notation (trial)
• Significant Figures (trial)
• Error Estimation (trial)
• Worked Example (trial)
• Worked Example (trial)
• Conceptual Insights (trial)
• Summary (trial)
• Practice Problems (trial)

Conclusion and Outlook

• Introduction (trial)
• Key Themes of the Book (trial)
• From Classical to Modern Physics (trial)
• Importance of Classical Mechanics (trial)
• Applications of Mechanics (trial)
• Skills Developed (trial)
• Suggested Next Steps (trial)
• Final Thoughts (trial)
• Closing Summary (trial)
• Practice Reflection (trial)