Lagrangian vs Hamiltonian Mechanics

Video Description

To learn for free on Brilliant, go to https://brilliant.org/AbideByReason/ . You’ll also get 20% off an annual premium subscription. There are 2 powerful analytical formulations of mechanics, Hamiltonian Mechanics and Lagrangian Mechanics. In this video, you'll learn how they are related to one another through the Legendre Transform. Along the way, we’ll also see that although Lagrangian and Hamiltonian Mechanics abandons the Newtonian geometric vector approach, an entirely new geometric view of physics emerges. _____ Join my (new) Patreon community: https://www.patreon.com/abidebyreason Support the channel with a one-time donation: https://ko-fi.com/abidebyreason _____ Previous video I made on Lagrangian Mechanics: https://youtu.be/_Hp11d1Z-78 _____ Sources: Making Sense of the Legendre Transform: https://arxiv.org/pdf/0806.1147 Great video covering similar topics: https://www.youtube.com/watch?v=0DHNGtsmmH8&t=825s Nice, short lecture on the Legendre Transform: https://www.youtube.com/watch?v=x2WXtvVtrUA&t=66s Classical Mechanics by John R. Taylor _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Illustrations and Thumbnails: Christine Kosakowski This video was sponsored by Brilliant