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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 second-order partial differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss-Russian mathematician Leonhard Euler and French-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.".
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- Euler–Lagrange_equation wikiPageWikiLinkText "Euler equation".
- Euler–Lagrange_equation wikiPageWikiLinkText "Euler–Lagrange equation".
- Euler–Lagrange_equation wikiPageWikiLinkText "Euler–Lagrange Equation".
- Euler–Lagrange_equation wikiPageWikiLinkText "Euler–Lagrange equation".
- Euler–Lagrange_equation wikiPageWikiLinkText "Euler–Lagrange equations of motion".
- Euler–Lagrange_equation wikiPageWikiLinkText "Lagrange framework".
- Euler–Lagrange_equation wikiPageWikiLinkText "Lagrange's equations".
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- Euler–Lagrange_equation id "1995".
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- Euler–Lagrange_equation title "Calculus of Variations".
- Euler–Lagrange_equation title "Euler-Lagrange Differential Equation".
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