% miko:type: atomic
% miko:title: Canonical Momentum
% miko:summary: Momentum defined by the Lagrangian, not always equal to mechanical momentum.
% miko:tags: mechanics
% miko:difficulty: undergrad
% miko:related: lagrangian-mechanics, hamiltonian-mechanics, noether-theorem
% miko:keywords: conjugate momentum, phase space, electromagnetic coupling

\documentclass{article}
\usepackage{amsmath}
\title{Canonical Momentum}
\begin{document}
\maketitle

\section{Definition}

For generalized coordinate $q_i$, canonical momentum is

$$
p_i = \frac{\partial L}{\partial \dot q_i}.
$$

\section{Interpretation}

Canonical momentum is the variable paired with $q_i$ in phase space. In the
presence of a vector potential, it can differ from mechanical momentum.

\end{document}
