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
- 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
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
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