This lecture introduces Lagrange's formulation of classical mechanics. That formulation is formal and elegant; it is based on the Least Action Principle. The concepts introduced here are central to all modern physics. Prof. Susskind discusses Lagrangian functions as they relate to coordinate systems and forces in a system. The lecture ends with angular momentum and coordinate transforms. Topics: - Principle of Least Action (“stationary action”) - Equilibrium points of a function - Trajectories - Calculus of variations - Light in a refractive media and hanging chain catenary - Lagrangian and Action - Euler Lagrange equations of motion - Newton equations from the Lagrangian of a system of particles - Importance of the Lagrange formulation of physics - Lagrangian and coordinate changes - Rotating frame, centrifugal and Coriolis forces - Polar coordinates and angular momentum conservation - Lagrangian, conservation and cyclic coordinates Recorded on October 10, 2011.

1. State diagrams and the Nature of Physical Laws
2. Newton's Law, Phase Space, Momentum and Energy
3. Lagrangian, Least Action & Euler-Lagrange Equations
4. Symmetry and Conservation Laws
5. The Hamiltonian
6. Hamilton's Equations
7. Liouville's Theorem & Phase Spaces
8. Poisson Brackets
9. Lagrangian of Static Electric and Magnetic Fields
10. Particles in Static Electric and Magnetic Fields

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.