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- Hamilton–Jacobi_equation abstract "In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton-Jacobi-Bellman equation. It is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi. In physics, it is a formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is particularly useful in identifying conserved quantities for mechanical systems, which may be possible even when the mechanical problem itself cannot be solved completely. The HJE is also the only formulation of mechanics in which the motion of a particle can be represented as a wave. In this sense, the HJE fulfilled a long-held goal of theoretical physics (dating at least to Johann Bernoulli in the 18th century) of finding an analogy between the propagation of light and the motion of a particle. The wave equation followed by mechanical systems is similar to, but not identical with, Schrödinger's equation, as described below; for this reason, the HJE is considered the "closest approach" of classical mechanics to quantum mechanics.".
- Hamilton–Jacobi_equation wikiPageID "897539".
- Hamilton–Jacobi_equation wikiPageRevisionID "592630861".
- Hamilton–Jacobi_equation subject Category:Hamiltonian_mechanics.
- Hamilton–Jacobi_equation subject Category:Partial_differential_equations.
- Hamilton–Jacobi_equation subject Category:Symplectic_geometry.
- Hamilton–Jacobi_equation comment "In mathematics, the Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations, and is a special case of the Hamilton-Jacobi-Bellman equation. It is named for William Rowan Hamilton and Carl Gustav Jacob Jacobi. In physics, it is a formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.".
- Hamilton–Jacobi_equation label "Ecuación de Hamilton-Jacobi".
- Hamilton–Jacobi_equation label "Equação de Hamilton–Jacobi".
- Hamilton–Jacobi_equation label "Hamilton-Jacobi-Formalismus".
- Hamilton–Jacobi_equation label "Hamilton-Jacobi-vergelijking".
- Hamilton–Jacobi_equation label "Hamilton–Jacobi equation".
- Hamilton–Jacobi_equation label "Równanie Hamiltona-Jacobiego".
- Hamilton–Jacobi_equation label "Teoria di Hamilton-Jacobi".
- Hamilton–Jacobi_equation label "Équations de Hamilton-Jacobi".
- Hamilton–Jacobi_equation label "Уравнение Гамильтона — Якоби".
- Hamilton–Jacobi_equation label "ハミルトン-ヤコビ方程式".
- Hamilton–Jacobi_equation label "哈密顿-雅可比方程".
- Hamilton–Jacobi_equation sameAs Hamilton%E2%80%93Jacobi_equation.
- Hamilton–Jacobi_equation sameAs Hamiltonova-Jacobiho_rovnice.
- Hamilton–Jacobi_equation sameAs Hamilton-Jacobi-Formalismus.
- Hamilton–Jacobi_equation sameAs Ecuación_de_Hamilton-Jacobi.
- Hamilton–Jacobi_equation sameAs Équations_de_Hamilton-Jacobi.
- Hamilton–Jacobi_equation sameAs Teoria_di_Hamilton-Jacobi.
- Hamilton–Jacobi_equation sameAs ハミルトン-ヤコビ方程式.
- Hamilton–Jacobi_equation sameAs 해밀턴-야코비_방정식.
- Hamilton–Jacobi_equation sameAs Hamilton-Jacobi-vergelijking.
- Hamilton–Jacobi_equation sameAs Równanie_Hamiltona-Jacobiego.
- Hamilton–Jacobi_equation sameAs Equação_de_Hamilton–Jacobi.
- Hamilton–Jacobi_equation sameAs Q1060137.
- Hamilton–Jacobi_equation sameAs Q1060137.
- Hamilton–Jacobi_equation wasDerivedFrom Hamilton–Jacobi_equation?oldid=592630861.