CM-03 Action Principle (Lecture Notes)

Prerequisites:Formulation of Euler Lagrange Equations fron Newton's Laws

Goals and Milestones:

1. Euler Lagrange equations follow from vartaional principle known as Hamilton's principle.
2. A symmetry transformation is a tansforamtion of generalized coordinates which leaves the Lagrangian invariant upto a total time derivative.
   
3. Noether's theorem states that there exists a conserved quantity corresponding to a every contnuous  transformation which is a symmetry transformation of the acton.
4. Learn about some well known conservation laws and corresponding symmetry transformation.
   
   

   Conservatiion of total momentum	Symmetry under translations
   Conservation of \(k^\text{th}\) component of total  angular momrntum	Symmetry under rotations about  \(k^\text{th}\) axis.
   In absence of exteral forces the centre of mass of a multipparticle system  moves with constant velocity.	Symmetry under Galiliean transformations.