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Physics · 术语表

什么是 Lagrangian and action?

Definition 1.3 University Physics — Year 3 · 第 1 章 — Lagrangian Mechanics

The Lagrangian of a mechanical system whose forces derive from a potential energy EpE_p is the function of the coordinates, the velocities, and possibly the time

L(q,q˙,t)=Ek−Ep,L(q, \dot q, t) = E_k - E_p ,

kinetic minus potential energy, both expressed in the generalized coordinates. The action of a conceivable motion q(t)q(t) between fixed endpoints q(t1)q(t_1) and q(t2)q(t_2) is the number

S[q]=∫t1t2L(q(t),q˙(t),t)  ⁣dt.S[q] = \int_{t_1}^{t_2} L\big(q(t), \dot q(t), t\big)\,\dd t .

SS is a functional: it eats a whole path and returns one number, in joule-seconds — the units of Planck’s constant.

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