Leonard Susskind focuses on symmetry and conservation laws, including the principle of least action and Lagrangian methods. He lectures on the relation between continuous symmetries of the Lagrangian and conserved quantities. Generalized coordinates and canonical conjugate momentum are introduced. Topics covered: - Symmetry and conservation laws: they are always related - Review of the principle of least action (stationary action) - Generalized coordinates and their canonical conjugate momentum - Conserved quantities and translation and rotation symmetry - Noether theorem concept and outline - Momentum conservation as a consequence of translation symmetry - Angular momentum conservation as a consequence of rotational symmetry - The harmonic oscillator - Discrete symmetries have no associated conserved quantities in classical mechanics Recorded on October 17, 2011.
This is the first course in a collection of 6 core physics courses by renowned physicist Leonard Susskind's series, The Theoretical Minimum. Our exploration of the theoretical underpinnings of modern physics begins with classical mechanics, the mathematical physics worked out by Isaac Newton (1642--1727) and later by Joseph Lagrange (1736--1813) and William Rowan Hamilton (1805--1865). We will start with a discussion of the allowable laws of physics and then delve into Newtonian mechanics. We then study three formulations of classical mechanics respectively by Lagrange, Hamiltonian and Poisson. Throughout the lectures we will focus on the relation between symmetries and conservation laws. The last two lectures are devoted to electromagnetism and the application of the equations of classical mechanics to a particle in electromagnetic fields.