Noether's Theorem

Every continuous symmetry brings a conservation law: shifts in time give energy, shifts in space give momentum, rotations give angular momentum

Noether's Theorem — Kepler's equal areas and the symmetries behind energy, momentum, angular momentum and charge, the three-line proof, orbits that lose a conservation law when a symmetry is broken, the Runge–Lenz vector and orbital precession, a pulse on a string with local energy balance, symmetry-preserving integrators, the pion anomaly and where conservation laws stop