**Physics Notes - Herong's Tutorial Notes** - v3.24, by Herong Yang

Physics Notes - Herong's Tutorial Notes

https://www.herongyang.com/Physics

Copyright © 2000-2022 Herong Yang. All rights reserved.

This book is a collection of notes on physics. Key sections are: What Is Space, Time and Speed; Frame of Reference; Coordinate Systems; Newton's Laws of Motion; Special Theory of Relativity; Time Dilation; Length Contraction; Minkowski spacetime; Lorentz transformation; Minkowski diagram; Hamiltonian and Lagrangian Mechanics; Generalized Coordinates; Phase Space and Phase Portrait. Updated in 2022 (Version v3.24) with minor changes.

Table of Contents

Meter Based on Earth's Meridian

Meter Based on Seconds Pendulum

Meter Prefixes and Other Units

List of Various Distances and Lengths

Introduction of Frame of Reference

Frame of Reference with 2 Objects

2-Dimensional Cartesian Coordinate System

3-Dimensional Cartesian Coordinate System

1 Frame of Reference with 2 Coordinate Systems

Second Prefixes and Other Units

Different Speeds Observed in Different Frames

Measuring Speed of Light - Roemer's Method

Measuring Speed of Light - Fizeau's Method

Measuring Speed of Light - Foucault's Method

Falling Ball in Earth Frame of Reference

Falling Ball in Elevator Frame of Reference

Introduction of Special Relativity

Assumptions of Special Relativity

What Is an Inertial Frame of Reference

The Constancy of the Speed of Light

Time Dilation in Special Relativity

Time Dilation - Moving Clock Is Slower

Demonstration of Time Dilation - Amy on the Train

Demonstration of Time Dilation - Bob on the Ground

Demonstration of Time Dilation - Formula

Elapsed Time between Distant Events

Length Contraction in Special Relativity

Length Contraction - Moving Object Is Shorter

Demonstration of Length Contraction

Length Contraction Formula and Lorentz Factor

Reciprocity of Length Contraction

The Relativity of Simultaneity

What Is the Relativity of Simultaneity

Formula for the Relativity of Simultaneity

Moving Frames and Galilean Transformation

Galilean Diagram of Moving Frames

Minkowski Spacetime and Diagrams

Hamiltonian on Free Fall Motion

Hamiltonian on Simple Harmonic Motion

Hamiltonian on Simple Pendulum Motion

Relation of Momentum and Hamiltonian

Hamiltonian in Cartesian Coordinates

Relation of Momentum and Potential Energy

Hamilton Equations in Cartesian Coordinates

Action - Integral of Lagrangian

Action - Functional of Position Function x(t)

Hamilton's Principle - Stationary Action

Other Proofs of the Lagrange Equation

Lagrange Equation on Free Fall Motion

Lagrange Equation on Simple Harmonic Motion

Lagrangian in Cartesian Coordinates

Lagrange Equations in Cartesian Coordinates

Introduction of Generalized Coordinates

Generalized Coordinates and Generalized Velocity

Simple Pendulum Motion in Generalized Coordinates

Hamilton's Principle in Generalized Coordinates

Lagrange Equations in Generalized Coordinates

Lagrange Equations on Simple Pendulum

What Is Legendre Transformation

Hamilton Equations in Generalized Coordinates

Phase Space and Phase Portrait

Phase Portrait of Simple Harmonic Motion

Phase Portrait of Pendulum Motion

Motion Equations of Linear Systems

**Keywords:** Physics, Space, Time, Speed, Mechanics, Relativity