Variational Principle
A fundamental physical principle asserting that true physical trajectories minimize or render stationary a scalar functional (such as action).
Governing formula
δ S = δ ∫_t₁^t₂ L(q, q̇, t) dt = 0 (Hamilton's Principle)
SI unit
Stationary Action Principle
In depth
Replaces force-based Newtonian mechanics with stationary action principles. In quantum mechanics, the Rayleigh-Ritz variational method provides upper bounds for ground state energies.
Examples in the real world
Deriving classical equations of motion via Fermat's principle of least time in optics and Hamilton's principle in mechanics.