% miko:type: atomic
% miko:title: Noether's Theorem
% miko:summary: Continuous symmetries of the action generate conserved quantities.
% miko:tags: mechanics
% miko:difficulty: undergrad
% miko:related: lagrangian-mechanics, euler-lagrange-equation, canonical-momentum
% miko:keywords: symmetry, conservation law, action

\documentclass{article}
\usepackage{amsmath}
\title{Noether's Theorem}
\begin{document}
\maketitle

\section{Core Idea}

If the action is invariant under a continuous transformation, then there is a
corresponding conserved quantity.

\section{Examples}

\begin{itemize}
\item Time translation symmetry gives energy conservation.
\item Spatial translation symmetry gives momentum conservation.
\item Rotational symmetry gives angular momentum conservation.
\end{itemize}

\section{Why It Matters}

Noether's theorem turns symmetry into a computational tool. It explains why
conservation laws are structural rather than accidental.

\end{document}
