In this lecture, Prof. Susskind looks closely at the concept of angular momentum and Poisson Brackets. He derives the basic angular momentum equations and shows how they can describe this fundamental type of motion. Poisson brackets are another formal formulation of classical mechanics. They help make the connection between symmetries and conservation laws more explicit. The Poisson bracket of the x,y,z components of angular momentum are derived. Topics covered: - Poisson brackets and angular momentum - Review of Poisson brackets - The algebra of Poisson brackets - Angular momentum conservation, rotation symmetry and Poisson brackets as tools to compute the generators of rotation - Momentum conservation, translation symmetry and Poisson brackets as tools to compute the generators of translation - Energy conservation, time shift symmetry and Poisson bracket as a tool to compute the time shift generator - General relation between symmetry and conservation law expressed with Poisson bracket. - Poisson brackets of the x, y, z components of angular momentum. - The gyroscope equations of motion as an example of the power of Poisson brackets Recorded on November 14, 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.