Euler 1744 / Lagrange 1755-60 — a functional S[q] = ∫_{t_1}^{t_2} L(q, q̇, t) dt is stationary under endpoint-fixed variations δq iff d/dt(∂L/∂q̇) − ∂L/∂q = 0 holds identically along the trajectory. Derivation: δS = ∫ (∂L/∂q·δq +…
Euler 1744 / Lagrange 1755-60 — a functional S[q] = ∫_{t_1}^{t_2} L(q, q̇, t) dt is stationary under endpoint-fixed variations δq iff d/dt(∂L/∂q̇) − ∂L/∂q = 0 holds identically along the trajectory. Derivation: δS = ∫ (∂L/∂q·δq +…