- Write the kinetic energy for a particle in projectile motion
- Write the potential energy for a particle in projectile motion
- We can now construct the Lagrangian . Use the Euler-Lagrange Equations () to find two conserved momenta and the equation of motion for free-fall.
- Can you see under what general condition momentum in a given direction will be conserved by studying the Euler-Lagrange Equations?

The fact that every differentiable symmetry of a Lagrangian yields a conserved quantity is known as Noether’s Theorem and was first proved by Emmy Noether in 1915. One of the founders of Abstract Algebra and a member of the GĂ¶ttingen school of Mathematics, she fled to the United States in 1933 after being expelled from her position by the Nazi party. A selection of biographies of Emmy Noether can be found here.