Physics Notes - Herong's Tutorial Notes

∟Introduction of Hamiltonian

This chapter provides an introduction of Hamiltonian. Topics include introduction of Hamiltonian; energy conservation; conservative system; free fall motion; simple harmonic motion; simple pendulum motion, momentum and Hamilton Equations.

What Is Hamiltonian

Hamiltonian on Free Fall Motion

Hamiltonian on Simple Harmonic Motion

Hamiltonian on Simple Pendulum Motion

What Is Momentum

Relation of Momentum and Hamiltonian

Hamiltonian in Cartesian Coordinates

Relation of Momentum and Potential Energy

Hamilton Equations in Cartesian Coordinates

Takeaways:

• Hamiltonian is defined as the total of kinetic and potential energy: H = T + V.
• Hamiltonian is a constant on a conservative system.
• Constant Hamiltonian on free fall motion gives a = g.
• Constant Hamiltonian on simple harmonic motion gives m*a = -k*x.
• Constant Hamiltonian on simple pendulum motion gives l*θ" = -g*sin(θ).
• Momentum p is defined as p = m*v.
• Momentum p is related to potential energy V as ∂V/∂r = -p'.
• Hamilton Equations are partial derivatives of Hamiltonian against position and momentum: ∂H/∂r = -p', ∂H/∂p = r'.

Table of Contents

 About This Book

 Introduction of Space

 Introduction of Frame of Reference

 Introduction of Time

 Introduction of Speed

 Newton's Laws of Motion

 Electromagnetic Fields

 Introduction of Light

 Speed of Light

 Introduction of Special Relativity

 Time Dilation in Special Relativity

 Length Contraction in Special Relativity

 The Relativity of Simultaneity

 Introduction of Spacetime

 Minkowski Spacetime and Diagrams

►Introduction of Hamiltonian

 Introduction of Lagrangian

 Introduction of Generalized Coordinates

 Phase Space and Phase Portrait

 Poisson Bracket Expression

 References

 Index

 Full Version in PDF/ePUB

Introduction of Hamiltonian - Updated in 2026, by Herong Yang