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Classical Mechanics (last updated: 2024 April 9)

Chapter 1. Centres of Mass

1.1	Introduction and Some Definitions
1.2	Plane Triangular Lamina
1.3	Plane Areas
1.4	Plane Curves
1.5	Summary of the Formulas for Plane Laminas and Curves
1.6	The Theorems of Pappus
1.7	Uniform Solid Tetrahedron, Pyramid and Cone
1.8	Hollow Cone
1.9	Hemispheres
1.10	Summary

Chapter 2. Moment of Inertia

2.1	Definition of Moment of Inertia
2.2	Meaning of Rotational Inertia
2.3	Moments of Inertia of Some Simple Shapes
2.4	Radius of Gyration
2.5	Plane Laminas and Mass Points distributed in a Plane
2.6	Three-dimensional Solid Figures. Spheres, Cylinders, Cones.
2.7	Three-dimensional Hollow Figures. Spheres, Cylinders, Cones.
2.8	Torus
2.9	Linear Triatomic Molecule
2.10	Pendulums
2.11	Plane Laminas. Product Moment. Translation of Axes (Parallel Axes Theorem).
2.12	Rotation of Axes
2.13	Momental Ellipse
2.14	Eigenvectors and Eigenvalues
2.15	Solid Body
2.16	Rotation of Axes - Three Dimensions
2.17	Solid Body Rotation. The Inertia Tensor.
2.18	Determination of the Principal Axes
2.19	Moment of Inertia with Respect to a Point
2.20	Ellipses and Ellipsoids
2.21	Tetrahedra

Chapter 3. Systems of Particles

3.1	Introduction
3.2	Moment of a Force
3.3	Moment of Momentum
3.4	Notation
3.5	Linear Momentum
3.6	Force and Rate of Change of Momentum
3.7	Angular Momentum
3.8	Torque
3.9	Comparison
3.10	Kinetic energy
3.11	Torque and Rate of Change of Angular Momentum
3.12	Torque, Angular Momentum and a Moving Point
3.13	The Virial Theorem

Chapter 4. Rigid Body Rotation

4.1	Introduction
4.2	Angular Velocity and Eulerian Angles
4.3	Kinetic Energy
4.4	Lagrange's Equations of Motion
4.5	Euler's Equations of Motion
4.6	Force-free Motion of a Rigid Asymmetric Top
4.7	Nonrigid Rotator
4.8	Force-free Motion of a Rigid Symmetric Top
4.9	Centrifugal and Coriolis Forces
4.10	The Top

Chapter 5. Collisions

5.1	Introduction
5.2	Bouncing Balls
5.3	Head-on Collision of a Moving Sphere with an Initially Stationary Sphere
5.4	Oblique Collisions
5.5	Oblique (Glancing) Elastic Collisions, Alternative Treatment
5.6	Two Colliding Rectangular Blocks

Chapter 6. Motion in a Resisting Medium

6.1	Introduction
6.2	Uniformly Accelerated Motion
6.3	Motion in which the Resistance is Proportional to the Speed
6.4	Motion in which the Resistance is Proportional to the Square of the Speed.

Chapter 7. Projectiles

7.1	No Air Resistance
7.2	Air Resistance Proportional to the Speed
7.3	Air Resistance Proportional to the Square of the Speed

Chapter 8. Impulsive Forces

8.1	Introduction
8.2	Problems

Chapter 9. Conservative Forces

9.1	Introduction
9.2	The Time and Energy Equation
9.3	Examples
9.4	Virtual Work

Chapter 10. Rocket Motion

10.1	Introduction
10.2	An Integral
10.3	The Rocket Equation
10.4	Problems

Chapter 11. Simple and Damped Oscillatory Motion

11.1	Simple Harmonic Motion
11.2	Mass Attached to an Elastic Spring
11.3	Torsion Pendulum
11.4	Ordinary Homogeneous Second-order Differential Equations
11.5	Damped Oscillatory Motion
11.6	Electrical Analogues

Chapter 12. Forced Oscillations

12.1	More on Differential Equations
12.2	Forced Oscillatory Motion
12.3	Electrical Analogue

Chapter 13. Lagrangian Mechanics

13.1	Introduction
13.2	Generalized Coordinates and Generalized Forces
13.3	Holonomic constraints
13.4	The Lagrangian Equations of Motion
13.5	Acceleration Components
13.6	Slithering Soap in Conical Basin
13.7	Slithering Soap in Hemispherical Basin
13.8	More Examples
13.9	Hamilton's Variational Principle

Chapter 14. Hamiltonian Mechanics

14.1	Introduction
14.2	A Thermodynamics Analogy
14.3	Hamilton's Equations of Motion
14.4	Examples
14.5	Poisson Brackets

Chapter 15. Special Relativity

15.1	Introduction
15.2	The Speed of Light
15.3	Preparation
15.4	Speed is Relative. The Fundamental Postulate of Special Relativity.
15.5	The Lorentz Transformations
15.6	But This Defies Common Sense
15.7	The Lorentz Transformation as a Rotation
15.8	Timelike and Spacelike 4-Vectors
15.9	The FitzGerald-Lorentz Contraction
15.10	Time Dilation
15.11	The Twins Paradox
15.12	A, B and C
15.13	Simultaneity
15.14	Order of Events, Causality and the Transmission of Information
15.15	Derivatives
15.16	Addition of Velocities
15.17	Aberration of Light
15.18	Doppler Effect
15.19	The Transverse and Oblique Doppler Effects
15.20	Acceleration
15.21	Mass
15.22	Momentum
15.23	Some Mathematical Results
15.24	Kinetic Energy
15.25	Addition of Kinetic Energies
15.26	Energy and Mass
15.27	Energy and Momentum
15.28	Units
15.29	Force
15.30	Electromagnetism

Chapter 16. Hydrostatics

16.1	Introduction
16.2	Density
16.3	Pressure
16.4	Pressure on a Horizontal Surface. Pressure at Depth z
16.5	Pressure on a Vertical Surface
16.6	Centre of Pressure
16.7	Archimedes' Principle
16.8	Some Simple Examples
16.9	Floating Bodies

Chapter 17. Vibrating Systems

17.1	Introduction
17.2	The Diatomic Molecule
17.3	Two Masses, Two Springs and a Brick Wall
17.4	Double Torsion Pendulum
17.5	Double Pendulum
17.6	Linear Triatomic Molecule
17.7	Two Masses, Three Springs, Two brick Walls
17.8	Transverse Oscillations of Masses on a Taut String
17.9	Vibrating String
17.10	Water
17.11	A General Vibrating System
17.12	A Driven System
17.13	A Damped Driven System

Chapter 18. The Catenary

18.1	Introduction
18.2	The Intrinsic Equation to the Catenary
18.3	Equation of the Catenary in Rectangular Coordinates, and Other Simple Relations
18.4	Area of a Catenoid

Chapter 19. The Cycloid

19.1	Introduction
19.2	Tangent to the Cycloid
19.3	The Intrinsic Equation to the Cycloid
19.4	Variations
19.5	Motion on a Cycloid, Cusps Up
19.6	Motion on a Cycloid, Cusps Down
19.7	The Brachystochrone Property of the Cycloid
19.8	Contracted and Extended Cycloids
19.9	The Cycloidal Pendulum
19.10	Examples of Cycloidal Motion in Physics

Chapter 20. Miscellanea

20.1

Introduction

20.2

Surface Tension

20.2.1	Excess Pressure Inside Drops and Bubbles
20.2.2	Angle of Contact
20.2.3	Capillary Rise

20.3

Shear Modulus and Torsion Constant

20.4

Viscosity

20.4.1	Poiseuille's Law
20.4.2	The Couette Viscometer

Chapter 21. Central Forces and Equivalent Potential

21.1	Introduction
21.2	Motion Under a Central Force
21.3	Inverse Square Attractive Force
21.4	Hooke’s Law
21.5	Inverse Fourth Power Attractive Force
21.6	A General Central Force
21.7	Inverse Cube Attractive Force

Chapter 22. Dimensions

22.1	Mass, Length and Time
22.2	Table of Dimensions
22.3	Checking Equations
22.4	Deducing Relationships
22.5	Dimensionless Quantities
22.6	Different Fundamental Quantities

Appendix A. Miscellaneous Problems

Appendix B. Solutions to Miscellaneous Problems