Classical Mechanics – Taylor Chapter 7 – Lagrange’s Equations

This is a lecture summarizing Taylor Chapter 7 – Lagrange’s Equations. This is part of a series of lectures for Phys 311 & 312 Classical Mechanics I & II for physics majors taught at the University of Tennessee, Knoxville. This is from one cold take of a physics lecture and is not heavily edited.

If you would like to review these topics at an introductory level please see videos for introductory classical mechanics from 2023

or older videos from 2022

Both of those playlists follow the OpenStax University Physics textbook.

0:00 Introduction to Lagrange’s Equations
10:25 Example: Particle in 2D in Polar Coordinates
16:53 Several Unconstrained Particles
21:06 Example of a Constrained System: Plane Pendulum
27:55 Constrained Coordinate System, Double Pendulum, Degrees of Freedom
40:40 Quick and Dirty Proof of Lagrange’s Equation
57:10 Example: Pulley with 2 Masses
1:43:00 Loop with a Bead Rotating in and Out of the Board
1:56:33 Loop with a Bead Rotating + Taylor Series
2:13:00 Generalized Momenta and Ignorable Coordinates
2:20:45 Conservation Laws
2:27:29 Derivation of the Hamiltonian from the Lagrangian
2:34:30 Example of the Hamiltonian
2:35:28 The Hamiltonian as Total Energy in Time-Independent Coordinates
2:43:45 Lagrangian for Magnetic Force
3:03:45 Lagrange Multipliers and Force Constraints