In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, Mécanique analytique. Lagrangian mechanics describes a mechanical system as a pair consisting of a configuration space and a smooth function within that space called a Lagrangian. By convention, where and are the kinetic and potential energy of the system, respectively. The stationary action principle requires that the action functional of the system derived from must remain at a stationary point (a maximum, minimum, or saddle) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. (Wikipedia).
There is a wholly alternative method for considering the time evolution of a system, not invoking causality or determinism, i.e. cause and effect or force and acceleration. Without using the laws of Newton we can use the principle of extremum (minimum) action to derive equations of motion
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Euler-Lagrange equation explained intuitively - Lagrangian Mechanics
Lagrangian Mechanics from Newton to Quantum Field Theory. My Patreon page is at https://www.patreon.com/EugeneK
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Physics 68 Lagrangian Mechanics (1 of 25) What is Lagrangian Mechanics?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is, when to use, and why do we need Lagrangian mechanics. Next video in this series can be seen at: https://youtu.be/uFnTRJ2be7I
From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS
Physics 68 Lagrangian Mechanics (3 of 25) The Partial Derivative W.R.T. Position
Visit http://ilectureonline.com for more math and science lectures! In this video I will show how the partial derivative of Lagrangian equation can be use in deriving the basic equations for free-fall, simple-harmonic-motion with spring, and coulomb's law equations. Next video in this se
From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS
The Beauty of Lagrangian Mechanics (SoME2 )
This video provides an introduction to the concepts in Lagrangian Mechanics, this will be the first in a series covering Lagrangian Mechanics, with the upcoming videos being more in-depth! This video is my submission for 3Blue1Brown's second summer math exhibition! Math animations made u
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Why Lagrangian Mechanics is BETTER than Newtonian Mechanics F=ma | Euler-Lagrange Equation | Parth G
Newtonian Mechanics is the basis of all classical physics... but is there a mathematical formulation that is better? In many cases, yes indeed there is! Lagrangian mechanics, named after Joseph Louis Lagrange, is a formulation of classical physics that is often more convenient to use than
From playlist 8.01 MIT Physics I - Classical Mechanics Dubbed in Turkish
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
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Lagrangian Mechanics I: Introducing the fundamentals
In this video, we discover the classical Lagrangian, the principle of stationary action and the Euler-Lagrange equation. For the best viewing experience, make sure to watch in full-screen and with 4K (2160p) resolution. Music in the background from https://www.FesliyanStudios.com Blackboa
From playlist Lagrangian Mechanics
Physics 68 Lagrangian Mechanics (4 of 25) Free Fall: Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will derive the position with-respect-to time equation of a simple free-fall problem using the partial derivative of Lagrangian equation. Next video in this series can be seen at: https://youtu.be/p5ThKn-
From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS
Lagrangian and Hamiltonian Mechanics in Under 20 Minutes: Physics Mini Lesson
There's a lot more to physics than F = ma! In this physics mini lesson, I'll introduce you to the Lagrangian and Hamiltonian formulations of mechanics. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up When you take your first physics class, you learn all ab
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Ch 12: What are generators in classical mechanics? | Maths of Quantum Mechanics
Hello! This is the twelfth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll take a detour into classical physics to learn about generators in the Lagrangian framework. We'll see that each physical quantity generates a change in the state of our particle, which wil
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What is General Relativity? Lesson 26: The central force problem in classical mechanics
What is General Relativity? Lesson 26: The central force problem in classical mechanics In this lesson we prepare ourselves for the study of the Schwarzschild geodesic analysis by doing a deep review of the Lagrangian formalism of classical mechanics with a particular focus on the central
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Lagrangian Mechanics: How powerful is it?
Check out Brilliant for 20% off: http://brilliant.org/ScienceAsylum Is Lagrangian mechanics powerful enough to replace Newton's laws? What does the principle of least action say about cause and effect (causality)? What the heck is an action? Let's find out! ________________________________
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Physics without Forces | Lagrangian Mechanics #SoME2
It is possible to rewrite all of physics in terms of energy. The video explains the theoretical motivations behind Lagrangian Mechanics, as well as how it leads to Noether's theorem applied on empty space. ------------------ Timestamps: 0:00 - Intro 1:18 - Newtonian Mechanics 2:34 - Newt
From playlist Summer of Math Exposition 2 videos
How to Come Up with the Semi-Implicit Euler Method Using Hamiltonian Mechanics #some2 #PaCE1
Notes for this video: https://josephmellor.xyz/downloads/symplectic-integrator-work.pdf When you first learn about Hamiltonian Mechanics, it seems like Lagrangian Mechanics with more work for less gain. The only reason we even learn Hamiltonian Mechanics in undergrad is that the Hamiltoni
From playlist Summer of Math Exposition 2 videos
Lecture 4 | Modern Physics: Special Relativity (Stanford)
Lecture 4 of Leonard Susskind's Modern Physics course concentrating on Special Relativity. Recorded May 5, 2008 at Stanford University. This Stanford Continuing Studies course is the first of a six-quarter sequence of classes exploring the essential theoretical foundations of modern phy
From playlist Lecture Collection | Modern Physics: Special Relativity
Physics 68 Lagrangian Mechanics (2 of 25) Why Does the Lagrangian Equation Work?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain why does the Lagrangian equation work in a simple free-fall example. Next video in this series can be seen at: https://youtu.be/RQexUJPnzOg
From playlist PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS
Special Relativity | Lecture 4
(April 30, 2012) Leonard Susskind moves into the topic of fields and field theory. For the most part he will focus on classical field theory, but occasionally will relate it to some of the concepts from quantum mechanics. In 1905, while only twenty-six years old, Albert Einstein publish
From playlist Lecture Collection | Special Relativity