Introduction to classical mechanics

Contents

Preface

1. Introduction

2. Vectors

3. Inertial Coordinate Systems

4. Newton’s Laws

5. Examples

6. Energy

7. Angular Momentum

8. System of Particles

9. Generalized Coordinates

10. Hamilton’s Principle

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

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
15.5 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

Walecka J. Introduction To Classical Mechanics. Solutions To Problems 2020.pdf