Introduction of Lagrangian
This chapter provides an introduction of Lagrangian Mechanics. Topics include introduction of Lagrangian; Action, Hamilton Principle, Stationary Action, Lagrange Equations, examples of free fall motion; simple harmonic motion, simple pendulum motion.
What Is Lagrangian
Action - Integral of Lagrangian
Action - Functional of Position Function x(t)
Hamilton's Principle - Stationary Action
What Is Lagrange Equation
Other Proofs of the Lagrange Equation
Lagrange Equation on Free Fall Motion
Lagrange Equation on Simple Harmonic Motion
Lagrangian in Cartesian Coordinates
Lagrange Equations in Cartesian Coordinates
- Lagrangian Function is defined as the difference of kinetic and potential energy: H = T - V.
- Action is defined as the integral of the Lagrangian function L(t)
between two time instances, t1 and t2.
- Hamilton's Principle states that the true position function x(t)
of a system is a stationary point of the Action S[x(t)] functional.
- Lagrange Equations state that the time derivative of
the partial derivative Lagrangian L against velocity
equals to the partial derivative Lagrangian L against position:
d(∂L/∂r')/dt = ∂L/∂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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