Classical Mechanics
Classical Mechanics (Fall 2007, Stanford 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. (from theoreticalminimum.com)
| Lecture 1 - State diagrams and the nature of physical laws A general discussion of the nature of the laws of physics and in particular classical mechanics. |
| Lecture 2 - Newton's laws, principle of least action Force and acceleration, Newton's laws, Kinetic energy and potential energy, Principle of least action. |
| Lecture 3 - Euler-Lagrange equations, symmetry and conservation laws Euler-Lagrange equations, Canonical momentum, Momentum conservation, Symmetry and conservation laws. |
| Lecture 4 - Symmetry and conservation laws This lecture focuses on the relation between continuous symmetries of the Lagrangian and conserved quantities. |
| Lecture 5 - Lagrangians and Hamiltonians Simple pendulum, Hamiltonian, kinetic and potential energy, Double pendulum, Hamiltonian formulation. |
| Lecture 6 - Hamilton's equations Energy conservation, Phase space, Canonical momentum, Poisson bracket, Hamilton's equations. |
| Lecture 7 - Liouville's theorem Liouville's theorem, Phase space, Magnetic field, Incompressible flow in phase space. |
| Lecture 8 - Motion in an electromagnetic field Least Action, Lorentz force equation, Electromagnetic equation of motion, Vector potential, Symmetries and conservation laws, Poisson brackets. |
| Lecture 9 - Poisson brackets formulation Poisson brackets, Canonical transformation, Phase space, Generator function. |
| References |
| Classical Mechanics (Fall, 2007) | 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). |
| Classical Mechanics Lecture Notes Classical Mechanics. Professor Leonard Susskind. The subject of this course is the relationship between symmetry and conservation laws. |