Geodesic
Some results in Lagrangian mechanics
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 591-603.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We associate to a dynamic equation $\xi$ three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities $\dot{q}$ are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.
Associamo ad un'equazione dinamica $\xi$ tre differenti connessioni e quindi consideriamo il significato dell'annullarsi della loro curvatura. Alcune peculiarità del caso di equazione dinamica autonoma polinomiale nelle velocità $\dot{q}$ vengono evidenziate. Finalmente, usando le cosiddette condizioni di Helmholtz, indaghiamo un particolare esempio. 
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Fiorani, Emanuele. Some results in Lagrangian mechanics. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 591-603. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a3/

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