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Some results in Lagrangian mechanics

Emanuele Fiorani — 2005

Bollettino dell'Unione Matematica Italiana

We associate to a dynamic equation $ξ$ 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.

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