Symmetries and Conservation Laws: Energy, Momentum and Angular Momentum Physics 6010, Fall 2010 Symmetries and Conservation Laws: Energy, Momentum and Angular Momentum Relevant Sections in Text: §2.6, 2.7 Symmetries and Conservation Laws

By a conservation law we mean a quantity constructed from the coordinates, velocities, accelerations, etc. of the system that does not change as the system evolves in time. When the equations of motion are second order, conservation laws typically arise as functions on the velocity phase (possibly with explicit time dependence). Conservation of energy, momentum and angular momentum are familiar examples. Conservation laws are also known as “constants of the motion”. They are allso called “first integrals” of the equations of motion. We will see why a little later. For example, consider a harmonic oscillator in one dimension. Let the generalized coordinate be x. The Lagrangian is