Leonard Susskind discusses the some of the basic laws and ideas of modern physics. In this lecture, he focuses on the motion of objects. He starts with a general example of a wedge on a frictionless plane and uses it as the building block for more complicated theory. - Motion of a ball on a wedge as an example of Euler-Lagrange equations - The ball on a wedge: Associated symmetries and conservation laws, conjugate momentum - Double pendulum example treated in detail. Associated symmetries and conservation - Hamiltonian, forbidden laws, reversibility, convergent and divergent paths in state space - Hamilton's equations of motion - Harmonic oscillator using Hamilton's equations and energy conservation - Phase space Recorded on November 1, 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.