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We study new Legendre transforms in classical mechanics and investigate someof their general properties. The behaviour of the new functions is analyzedunder coordinate transformations.When invariance under different kinds oftransformations are considered, the new formulation is found to be completlyequivalent to the usual Lagrangian formulation, recovering well establishedresults like the conservation of the angular momentum. Furthermore, a naturalgeneralization of the Poisson Bracket is found to be inherent to the formalismintroduced. On the other hand, we find that with a convenient redefinition ofthe Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible toestablish an exact one-to-one mathematical correspondence between thethermodynamic potentials and the new potentials of classical mechanics

An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics