https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Euler-Lagrange_equation_of_a_functionalEuler-Lagrange equation of a functional - Revision history2026-09-30T22:51:48ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Euler-Lagrange_equation_of_a_functional&diff=453&oldid=prevVipul: 1 revision2008-05-18T19:39:49Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://diffgeom.subwiki.org/w/index.php?title=Euler-Lagrange_equation_of_a_functional&diff=452&oldid=prevVipul at 10:21, 5 August 20072007-08-05T10:21:31Z<p></p>
<p><b>New page</b></p><div>==Definition==<br />
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Let <math>M</math> be a [[differential manifold]] and <math>\Omega(M;p,q)</math> be the [[path space]] viz the space of [[piecewise smooth path]]s from <math>p</math> to <math>q</math> in <math>M</math>. Let <math>F:\Omega \to \R</math> be a functional.<br />
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The Euler-Lagrange equation is the equation that <math>\omega \in \Omega</math> needs to satisfy to be a [[critical path of a functional|critical path]] of <math>F</math>, viz, the equation it must satisfy so that for ''every'' piecewise smooth variation <math>W</math> of <math>\omega</math>, the derivative of <math>F</math> along <math>W</math> is zero.</div>Vipul