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Curated by: Dr. Jorge S. Diaz (58 videos)
Go to lovable.dev to start building today and use my code JKZEROYT20 for 20% off in the first purchase of the Pro plan. Direct link: https://lovable.link/jorgediazyt Buy me a coffee and support the channel: https://ko-fi.com/jkzero In this video, I present one of the most elegant formulations of physics — Lagrangian mechanics. Born from the genius of Joseph-Louis Lagrange in the 18th century, this framework redefined how we think about motion — not through forces, but through energy and the principle of stationary action. Starting from Newtonian mechanics, I show you how to derive Hamilton’s principle, answering a common question "why is the Lagrangian kinetic minus potential energy?" Then we derive the Lagrange equations, and see how a single idea unifies classical mechanics into a clean, mathematical structure. [Related videos] ∘ This is how Heisenberg created quantum mechanics https://youtu.be/oVzzIkkYGY8 ∘ Playlist Heisenberg's Matrix Mechanics https://www.youtube.com/playlist?list=PL_UV-wQj1lvXuBvDHjqhnReMHoqgR8nQi ∘ Playlist video series on Quantum Physics https://www.youtube.com/playlist?list=PL_UV-wQj1lvVxch-RPQIUOHX88eeNGzVH ∘ Lagrangian Mechanics I: Introducing the fundamentals by Physics Fluency https://www.youtube.com/watch?v=drZGeAkN4QI ∘ Lagrangian vs Newtonian Mechanics by Abide By Reason https://youtu.be/_Hp11d1Z-78?si=cCgkk_TJu0_g4TNJ [Errata] 15:55 right-hand side of the second line says "d(q̈ δq̇)/dt" but it should say "d(q̇ δq)/dt" Thanks @quoc-trungho2349 for notifying this 27:10 the right-hand side of the commutation relation is missing a minus sign, it should say "[p,q] = −ih Thanks @alexmuresan7183 for notifying this. [References] ∘ M. Born and P. Jordan, "Zur Quantenmechanik,” Z. Phys. 34, 858 (1925) ∘ J. L. Lagrange, "Mécanique Analytique" (1835) ∘ W. R. Hamilton, "On a general method in dynamics," Phil. Trans. R. Soc.124, 247 (1834) ∘ W. R. Hamilton, "Theory of Systems of Rays," Trans. R. Ir. Acad. 15, 69 (1828) [Credits] Philosophiae Naturalis Principia Mathematica by P. Hermans under CC BY-SA 3.0 Philosophiae Naturalis Principia Mathematica by UCL under CC BY 2.0 Force diagrams by W.J.'s Gravesande, public domain Mathematical elements of natural philosophy, confirm'd by experiments Notes on QFT by J.S. Diaz Lagrangian of the Standard Model of particle physics, public domain Close up on coding on laptop by Raddy, free use via Pexels https://www.pexels.com/video/close-up-on-coding-on-laptop-screen-11274330/ Vibrating Drumhead by LunarEclipse2014, public domain Double pendulum simulation by Zvika, public domain Simulation of Kelvin-Helmholtz instability by Bdubb12, public domain Pierre_Varignon, public domain Portrait of Gottfried Leibniz, Herzog Anton Ulrich Museum, public domain Johann Bernoulli, public domain Jakob Hermann, public domain Daniel Bernoulli by Bammesk under Leonhard Euler, public domain Alexis Clairaut, public domain Jean Le Rond d'Alembert, public domain Pierre Louis Maupertuis, public domain Joseph Louis Lagrange, public domain Lagrange's Analytical Mechanics, public domain William Rowan Hamilton, public domain Euler-Lagrange equation graffiti by J.S. Diaz Feynman Lectures on Physics, Caltech Harmonic oscillator by I. Airola under CC BY-SA 4.0 Deed Portrait of Erwin Schrodinger, AIP L. de Broglie, public domain Moon transiting the Earth by D.J. Lindler, Sigma Space Corporation and NASA/JPL-Caltech/GSFC/UMD, public domain Solar system by Datumizer under CC BY-SA 4.0 Potrait of Emmy Noether under CC BY-SA 4.0 AIP: American Institute of Physics, Emilio Segrè Visual Archives CC BY 2.0 https://creativecommons.org/licenses/by/2.0/deed.en CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/deed.en CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0/deed.en CC BY-SA 4.0 Deed https://creativecommons.org/licenses/by-sa/4.0/