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Moving Frames and Conservation Laws for Euclidean Invariant Lagrangians


T. M. N. Gonçalves, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, UK; e-mail:


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 SE(2) and SE(3).