Moving Frames and Conservation Laws for Euclidean Invariant Lagrangians. Issue 2 (9th August 2012)

• Record Type: Journal Article
• Authors: Gonçalves, T. M. N.; Mansfield, E. L.
• Is Part Of: Studies in applied mathematics. Volume 130:Issue 2(2013)
• Page Start: 134
• Page End: 166
• Publication Date: 2012-08-09
• Subjects: Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathématique; Mathématique appliquée; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519
• DOI: 10.1111/j.1467-9590.2012.00566.x
• Languages: English
• ISSNs: 0022-2526

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>In recent work, the authors show the mathematical structure behind both the Euler–Lagrange system and the set of conservation laws, in terms of the differential invariants of the group action and a moving frame. In this paper, the authors demonstrate that the knowledge of this structure allows to find the first integrals of the Euler–Lagrange equations, and subsequently, to solve by quadratures, variational problems that are invariant under the special Euclidean groups <italic>SE</italic>(2) and <italic>SE</italic>(3).</p> </abstract>