Classical Mechanics

10/29/2007

Stanford class with Leonard Susskind.

The Euler-Lagrange Equations

Minimizing the action results in the Euler-Lagrange Equations

The canonical momentum conjugate to the coordinate is

The force is

so that

Conservation of momentum

Note that only the differences appear in the potential.

the conservation of momentum follows.

The conservation law results from a continuous symmetry: a translation.

Example: falling object

since

since

Example: polar coordinates velocity components, conservation of angular momentum

Kinetic Energy

When

then angular momentum is constant