We show that the canonical semispray of a regular Lagrangian of order k is uniquely determined by two associated Cartan–Poincaré one-forms. Equivalently, the canonical semispray is uniquely determined by its canonical presymplectic structure and one of the Cartan–Poincaré one-forms. We prove that this order vector field is determined by a variational problem, for which only the vertical part of the curve is varied.
Nous obtenons que la sémi-gerbe canonique d'un Lagrangien régulier d'ordre k est uniquement déterminée par deux un-formes Cartan–Poincaré associées. Autrement dit, la sémi-gerbe canonique est uniquement déterminée par sa structure présimplectique canonique et par une des une-formes Cartan–Poincaré. Nous prouvons que ce champ de vecteurs d'ordre est déterminée par un problème variationel pour lequel seulement la partie verticale de la courbe varie.
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@article{CRMATH_2007__345_5_269_0, author = {Bucataru, Ioan}, title = {Canonical semisprays for higher order {Lagrange} spaces}, journal = {Comptes Rendus. Math\'ematique}, pages = {269--272}, publisher = {Elsevier}, volume = {345}, number = {5}, year = {2007}, doi = {10.1016/j.crma.2007.07.027}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.07.027/} }
TY - JOUR AU - Bucataru, Ioan TI - Canonical semisprays for higher order Lagrange spaces JO - Comptes Rendus. Mathématique PY - 2007 SP - 269 EP - 272 VL - 345 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.07.027/ DO - 10.1016/j.crma.2007.07.027 LA - en ID - CRMATH_2007__345_5_269_0 ER -
Bucataru, Ioan. Canonical semisprays for higher order Lagrange spaces. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 269-272. doi : 10.1016/j.crma.2007.07.027. http://archive.numdam.org/articles/10.1016/j.crma.2007.07.027/
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