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The Journal of Geometric Mechanics (JGM)
 

Bundle-theoretic methods for higher-order variational calculus

Pages: 99 - 120, Volume 6, Issue 1, March 2014      doi:10.3934/jgm.2014.6.99

 
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Michał Jóźwikowski - Institute of Mathematics. Polish Academy of Sciences, Śniadeckich 8, PO box 21, 00-956 Warsaw, Poland (email)
Mikołaj Rotkiewicz - Institute of Mathematics. Polish Academy of Sciences, Śniadeckich 8, PO box 21, 00-956 Warsaw, Poland (email)

Abstract: We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.

Keywords:  Higher tangent bundles, variational calculus, higher-order Euler-Lagrange equations, graded bundles, integration by parts, geometric mechanics.
Mathematics Subject Classification:  58A20, 58E30, 70H50.

Received: August 2013;      Revised: February 2014;      Available Online: April 2014.

 References