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Remarks on dissipation in lagrange formalism and attempts to overcome the difficulties

Anthony K. H.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

1998

Z. 66

55-77

In its first part this paper presents a principle discussion on the relation between Lagrange formalism in the strict sense of Hamilton's Principle of Least Action and the inverse problem of variational calculus. This discussion is necessary because of a big confusion in literature. It is inevitable with regard to the unification of different physical systems within Lagrange formalism. Especially for dissipation as described by means of Lagrange formalism this problem is essential. The second part of the paper os concerned with dissipation in mechanical systems. The mechanics of a mass point suffering from a frictional force is implied into Lagrange formalism as a complete thermo-mechanical theory: Dissipation is associated with an irreversible energy transfer from mechanical to thermal degrees of freedom. Formally this is realized by introducing transfer variables. In this way friction is described phenomenologically in more details than is traditionally done by means of friction coefficients. Physical interpretations of the transfer variables are propsed. The theory is constructed along a methodical line which has already successfully been applied for Thermodynamics of Irreversible Processes.