This lecture focuses on the relation between continuous symmetries of the Lagrangian and conserved quantities. Generalized coordinates and canonical conjugate momentum are introduced.

Topics: 

• Symmetry and conservation laws: they are always related

• Review of the principle of least action (stationary action)

• Generalized coordinates and their canonical conjugate momentum

• Conserved quantities and translation and rotation symmetry

• Noether theorem concept and outline

• Momentum conservation as a consequence of translation symmetry

• Angular momentum conservation as a consequence of rotational symmetry

• The harmonic oscillator

• Discrete symmetries have no associated conserved quantities in classical mechanics

• References:

• Symmetry and conservation laws

• Noether’s theorem

• Harmonic oscillator

• Generalized coordinates

• Angular momentum conservation