力学 · 学部

Canonical Momentum

Momentum defined by the Lagrangian, not always equal to mechanical momentum.

公開 2026年4月26日 · 1 分

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Definition

For generalized coordinate $q_i$ , canonical momentum is

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

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.

Dynamics on phase space using coordinates and conjugate momenta.

最小作用の原理から運動方程式を導く、解析力学の出発点。

Continuous symmetries of the action generate conserved quantities.