Classical Mechanics
Classical Mechanics (Fall 2011, Standard Univ.). Instructor: Professor Leonard Susskind. 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. (from theoreticalminimum.com)
| Lecture 01 - State diagrams and the nature of physical laws A brief introduction to the mathematics behind physics including the addition and multiplication of vectors as well as velocity and acceleration in terms of particles. |
| Lecture 02 - Newton's law, phase space, momentum and energy Aristotle incorrect laws of motion, Newton's 2nd law, Phase space, Newton's 3 laws, Conservation of momentum, Energy conservation. |
| Lecture 03 - Lagrangian, least action, Euler-Lagrange equations Principle of Least Action, Euler-Lagrange equations of motion, Lagrangian and Action, Lagrangian and coordinate changes, Angular momentum conservation. |
| Lecture 04 - Symmetry and conservation laws Symmetry and conservation laws, Review of the principle of least action, Generalized coordinates, Canonical conjugate momentum, Noether theorem, Momentum conservation. |
| Lecture 05 - The Hamiltonian Review of symmetries and conservation laws, Energy conservation as a consequence of time translation symmetry, Hamiltonian and energy conservation. |
| Lecture 06 - Hamilton's equations Many mechanical practical examples, Hamilton's equations of motion, Harmonic oscillator using Hamilton's equations and energy conservation, Phase space. |
| Lecture 07 - Liouville's theorem Liouville's theorem, Review of Hamiltonian and energy conservation, Flow in phase space, Demonstration of Liouville's theorem, Liouville using a toy Hamiltonian, Poisson brackets. |
| Lecture 08 - Poisson brackets Poisson brackets, The algebra of Poisson brackets, General relation between symmetry and conservation law expressed with Poisson bracket, Poisson brackets of the x, y, z components of angular momentum. |
| Lecture 09 - Electric and magnetic fields 1 Magnetic and electric fields, The vector potential, Gauge field, Lorentz force, Lagrangian for charged particles in a electro-static and magneto-static fields, Gauge invariance. |
| Lecture 10 - Electric and magnetic fields 2 A general review of all the concepts learned so far applied to a particle in electric and magnetic static fields. |
| References |
| Classical Mechanics (Fall, 2011) | 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). |