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- Euler–Lagrange_equation abstract "In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation although the latter name is ambiguous (see disambiguation page), is a differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange in the 1750s.Because a differentiable functional is stationary at its local maxima and minima, the Euler–Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing (or maximizing) it. This is analogous to Fermat's theorem in calculus, stating that at any point where a differentiable function attains a local extremum, its derivative is zero.In Lagrangian mechanics, because of Hamilton's principle of stationary action, the evolution of a physical system is described by the solutions to the Euler–Lagrange equation for the action of the system. In classical mechanics, it is equivalent to Newton's laws of motion, but it has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.".
- Euler–Lagrange_equation wikiPageID "294995".
- Euler–Lagrange_equation wikiPageRevisionID "605281807".
- Euler–Lagrange_equation backgroundColour "#ECFCF4".
- Euler–Lagrange_equation borderColour "#50C878".
- Euler–Lagrange_equation id "1995".
- Euler–Lagrange_equation id "p/l057150".
- Euler–Lagrange_equation indent ":".
- Euler–Lagrange_equation title "Calculus of Variations".
- Euler–Lagrange_equation title "Euler-Lagrange Differential Equation".
- Euler–Lagrange_equation title "Lagrange equations".
- Euler–Lagrange_equation urlname "Euler-LagrangeDifferentialEquation".
- Euler–Lagrange_equation subject Category:Articles_containing_proofs.
- Euler–Lagrange_equation subject Category:Calculus_of_variations.
- Euler–Lagrange_equation subject Category:Ordinary_differential_equations.
- Euler–Lagrange_equation subject Category:Partial_differential_equations.
- Euler–Lagrange_equation comment "In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation although the latter name is ambiguous (see disambiguation page), is a differential equation whose solutions are the functions for which a given functional is stationary.".
- Euler–Lagrange_equation label "Ecuaciones de Euler-Lagrange".
- Euler–Lagrange_equation label "Equazioni di Eulero-Lagrange".
- Euler–Lagrange_equation label "Equação de Euler-Lagrange".
- Euler–Lagrange_equation label "Euler–Lagrange equation".
- Euler–Lagrange_equation label "Równania Eulera-Lagrange’a".
- Euler–Lagrange_equation label "Équation d'Euler-Lagrange".
- Euler–Lagrange_equation label "Уравнение Эйлера — Лагранжа".
- Euler–Lagrange_equation label "オイラー=ラグランジュ方程式".
- Euler–Lagrange_equation label "歐拉-拉格朗日方程".
- Euler–Lagrange_equation sameAs Euler%E2%80%93Lagrange_equation.
- Euler–Lagrange_equation sameAs Eulerova-Lagrangeova_rovnice.
- Euler–Lagrange_equation sameAs Εξίσωση_Όιλερ-Λαγκράνζ.
- Euler–Lagrange_equation sameAs Ecuaciones_de_Euler-Lagrange.
- Euler–Lagrange_equation sameAs Équation_d'Euler-Lagrange.
- Euler–Lagrange_equation sameAs Equazioni_di_Eulero-Lagrange.
- Euler–Lagrange_equation sameAs オイラー=ラグランジュ方程式.
- Euler–Lagrange_equation sameAs 오일러-라그랑주_방정식.
- Euler–Lagrange_equation sameAs Euler-lagrange-vergelijking.
- Euler–Lagrange_equation sameAs Równania_Eulera-Lagrange’a.
- Euler–Lagrange_equation sameAs Equação_de_Euler-Lagrange.
- Euler–Lagrange_equation sameAs Q875744.
- Euler–Lagrange_equation sameAs Q875744.
- Euler–Lagrange_equation wasDerivedFrom Euler–Lagrange_equation?oldid=605281807.