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

Hamilton Equations in Generalized Coordinates

This section provides a quick introduction to Hamilton Equations in Generalized Coordinates.

With the definition of generalized momentum p, Hamilton Equations in generalized coordinates stays in the same form as in Cartesian coordinates:

∂H/∂q = -p' (C.6) ∂H/∂p = q' (C.7) # q is the generalized position # p is the generalized momentum

Table of Contents

Introduction of Frame of Reference

Introduction of Special Relativity

Time Dilation in Special Relativity

Length Contraction in Special Relativity

The Relativity of Simultaneity

Minkowski Spacetime and Diagrams

►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