Summary
We prove that for first-order differential systems the set ofS-equivalent transformations of Lagrangians coincides with the set of symmetry transformations of their equations of the motion. Noetherian symmetries are never enough to cover the whole set of symmetries of dynamical equations, even if the equations are of first order.
Riassunto
Si prova che per sistemi differenziali di prim’ordine il gruppo di trasformazioni di equivalenzaS delle lagrangiane coincide con il gruppo di trasformazioni di simmetria delle loro equazioni di moto. Le simmetrie noetheriane non sono mai sufficienti a capire l’intero gruppo di simmetrie di equazioni dinamiche, anche se le equazioni sono di prim’ordine.
Резюме
Мы доказываем, что для дифференциальных систем первого порядка системаS-эквивалентных преобразований Лагранжианов совпадает с системой симметричных преобразований уравнений движения. Симметрии Ноэтера никогда не покрывают всю систему симметрий динамических уравнений, даже если уравнения являются уравнениями первого порядка.
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On sabbatical leave from Centro de Estudios Nucleares, Universidad Nacional Autonoma de Mexico, Circuito Exterior, C.U., 04510 Mexico, D.F., Mexico.
Traduzione a cura della Redazione.
Перевебено ребакцией.
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Hojman, S., Zertuche, F. S-equivalence and symmetries of first-order differential systems. Nuov Cim B 88, 1–8 (1985). https://doi.org/10.1007/BF02729024
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DOI: https://doi.org/10.1007/BF02729024