On the Lagrangian being a homogeneous function of the velocity

Gaetano Giaquinta


In this contribution a careful critical reading of the feasibility to express a Lagrangian function as the sum of several terms each having a different degree of homogeneity with respect to the velocities is presented. Arguments are proposed so to overcome some of the involved difficulties, addressing to visualize a dynamical evolution process of a system of given Lagrangian L when interacting with an environment as the breaking of the degree of homogeneity with respect to the velocities of the Lagrangian itself due to the dynamical coupling to the environment. Specific attention is devoted to systems the Lagrangians of which are of degree of homogeneity equal to one.


Lagrangian,Equations of motion,Energy

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DOI: http://dx.doi.org/10.1478/AAPP.91S2A4

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