Summary
An extension of the second Noether theorem is proposed, which covers the case of Lagrangians invariant under local transformations of the velocities without any related co-ordinate transformation. A set of true Lagrangian transformations can be associated to such invariances and it is found that the Noether identities imply Lagrangian constraints.
Riassunto
Si propone un'estensione del secondo teorema di Noether, che considera il caso di lagrangiane invarianti sotto trasformazioni locali delle velocità, cui non sono associate trasformazioni delle coordinate. A tali invarianze possono associarsi delle vere trasformazioni lagrangiane e si trova che le identità di Noether implicano vincoli lagrangiani.
Резюме
Предлагается обобЩение второй теоремы Ноэтера, которое охватывает случай Лагранжианов, инвариантных относительно локальных преобразований скоростей без преобразования координат. Система преобразований ЛагранжианоВ может быть связана с такой инвариантностью и обнаружено, что тождества Ноэтера подразумевают ограничения Лагранжиана.
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Lusanna, L. An extension of the second noether theorem. Nuov Cim B 52, 141–150 (1979). https://doi.org/10.1007/BF02739029
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DOI: https://doi.org/10.1007/BF02739029