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