Introduction to Classical Mechanics

✍ Scribed by John Dirk Walecka

• Publisher: WSPC
• Year: 2020
• Tongue: English
• Leaves: 184
• Category: Library

✦ Synopsis

This textbook aims to provide a clear and concise set of lectures that take one from the introduction and application of Newton's laws up to Hamilton's principle of stationary action and the lagrangian mechanics of continuous systems. An extensive set of accessible problems enhances and extends the coverage.

It serves as a prequel to the author's recently published book entitled Introduction to Electricity and Magnetism based on an introductory course taught sometime ago at Stanford with over 400 students enrolled. Both lectures assume a good, concurrent, course in calculus and familiarity with basic concepts in physics; the development is otherwise self-contained.

A good introduction to the subject allows one to approach the many more intermediate and advanced texts with better understanding and a deeper sense of appreciation that both students and teachers alike can share.

✦ Table of Contents

Contents
Preface
1. Introduction
1.1 Physics
1.2 Calculus
1.3 Example
1.4 Units
2. Vectors
2.1 Vector
2.2 Scalar Product
2.3 Vector Product
2.4 Length and Direction
2.5 Gradient
2.5.1 Example −!∇V (r)
3. Inertial Coordinate Systems
4. Newton’s Laws
5. Examples
5.1 Spring
5.2 Projectile Motion
5.3 Two-Body Problem
6. Energy
6.1 Spring
6.2 Projectile Motion
6.3 Two-Body Problem
6.3.1 Conservative Force
6.3.2 Two-Body System
7. Angular Momentum
7.1 Angular Momentum
7.2 Uniform Circular Motion
7.2.1 Gravitational Orbits
8. System of Particles
8.1 C-M Motion
8.2 Energy
8.3 Angular Momentum
8.4 Rigid-Body Motion
9. Generalized Coordinates
9.1 Pendulum
9.2 Particle on Table Connected to Hanging Mass
9.3 Bead on a Rotating Hoop
9.4 Coupled Oscillators
10. Hamilton’s Principle
10.1 Calculus of Variations
10.2 Hamilton’s Principle
10.3 Lagrange’s Equation
11. Lagrangian Dynamics
11.1 Examples
11.1.1 Another Bead on a Rotating Hoop
11.1.2 Cylinder Rolling on Incline Plane
11.2 Canonical Momentum
11.3 Hamiltonian
11.4 Previous Examples
12. Hamiltonian Dynamics
12.1 Hamilton’s Principle
12.2 Hamilton’s Equations
13. Continuum Mechanics
13.1 Oscillations of Particles Connected by Springs
13.2 Continuum Limit
13.3 Wave Equation for String
13.3.1 Normal Modes
13.3.2 Boundary Conditions
13.3.3 General Solution
14. Waves
14.1 One-Dimensional Wave Equation
14.2 Superposition
14.3 Traveling Waves
14.3.1 Snapshot at Fixed t
14.3.2 Disturbance at a Fixed x
14.4 Standing Waves
14.5 Amplitude Modulation
15. Continuum Mechanics of String
15.1 Energy
15.2 Lagrangian
15.3 Lagrange’s Equation
15.4 Hamilton’s Principle
15.5 Lagrangian Dynamics
15.5.1 Canonical Momentum Density
15.5.2 Hamiltonian Density
15.5.3 Continuity Equation
15.5.4 Momentum Density
15.6 Energy-Momentum Tensor
16. Mechanics of Fluids
16.1 Assumptions
16.2 Lagrangian Density
16.3 Lagrange’s Equations
16.3.1 Continuity Equation
16.3.2 Energy Flux
16.3.3 Bernoulli’s Theorem
16.4 Sound Waves
16.5 Sound Spectrum
17. Problems
Appendix A Numerical Methods
Appendix B Significant Names in Classical Mechanics
Bibliography
Index