Hamiltonian optics
Hamiltonian optics and Lagrangian optics are two formulations of geometrical optics which share much of the mathematical formalism with Hamiltonian mechanics and Lagrangian mechanics. == Hamilton's principle == In physics, Hamilton's principle states that the evolution of a system ( q 1 ( σ ) , … , q N ( σ ) ) {\displaystyle \left(q_{1}{\left(\sigma \right)},\dots ,q_{N}{\left(\sigma \right)}\right)} described by N {\displaystyle N} generalized coordinates between two specified states at two specified parameters σA and σB is a stationary point (a point where the variation is zero) of the action functional, or δ S = δ ∫ σ A σ B L ( q 1 , ⋯ , q N , q ˙ 1 , ⋯ , q ˙ N , σ ) d σ = 0 {\displaystyle \delta S=\delta \int _{\sigma _{A}}^{\sigma _{B}}L\left(q_{1},\cdots ,q_{N},{\dot {q}}_{1},\cdots ,{\dot {q}}_{N},\sigma \right)\,d\sigma =0} where q ˙ k = d q k / d σ {\displaystyle {\dot {q}}_{k}=dq_{k}/d\sigma } and L {\displaystyle L} is the Lagrangian.