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

 About This Book

 Introduction of Space

 Introduction of Frame of Reference

 Introduction of Time

 Introduction of Speed

 Newton's Laws of Motion

 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

 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 Generalized Momentum

 What Is Legendre Transformation

Hamilton Equations in Generalized Coordinates

 Phase Space and Phase Portrait


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