Inverse problem in classical mechanics: Dissipative systems
It is well-known that a system of differential equations describing the motion of a classical mechanical systems does not determine a unique Lagrangian from which it arises. Clearly such different Lagrangian descriptions of the same system also give rise to different Hamiltonians or 'energies', and it turns out that whether a dynamical system is dissipative or not may depend on its Lagrangian description. The paper under review addresses this problem, and shows the geometric origin of Lagrangians describing dissipative systems, in the context of global differential geometry. In particular, a general procedure is also described to give a Lagrangian description for a class of dissipative systems, and a section is devoted to the cosideration of ambiguity in the Lagrangian description to cover different dissipative forces. Noether's theorem in such a setting is also briefly touched upon. The paper contains a very useful rather detailed list of references.
scientific article; zbMATH DE number 3915686
scientific article