6533b872fe1ef96bd12d304d

RESEARCH PRODUCT

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

Ginés R. Pérez Teruel

subject

PhysicsLegendre transformationsymbols.namesakeAngular momentumFormalism (philosophy of mathematics)Poisson bracketClassical mechanicssymbolsGeneral Physics and AstronomyAnalogyLagrangianGeneral Relativity and Quantum CosmologyThermodynamic potential

description

We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an exact one-to-one mathematical correspondence between the thermodynamic potentials and the new potentials of classical mechanics

10.1088/0143-0807/34/6/1589http://arxiv.org/abs/1309.5510