Canonical coordinates are a set of position and momentum variables used in classical mechanics, typically denoted as $(q_i, p_i)$, that form the foundation for Hamiltonian mechanics. These coordinates provide a systematic way to describe the state of a mechanical system and facilitate the formulation of Hamilton's equations, which describe the evolution of a system over time. By transforming from Lagrangian to Hamiltonian formalism through the Legendre transformation, canonical coordinates allow for a clearer understanding of dynamics in both classical and quantum contexts.
congrats on reading the definition of canonical coordinates. now let's actually learn it.