Inverse problem in classical mechanics: Dissipative systems
type: Item
instance of: scholarly article
title: Inverse problem in classical mechanics: Dissipative systems
zbMATH Open document ID: 0573.70014
DOI: 10.1007/BF02080477
author: G. Platania
author: Ruggiero de Ritis
author: Giuseppe Marmo
author: Paolo Scudellaro
published in: International Journal of Theoretical Physics
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 3915686
zbMATH Keywords: equivalent Lagrangians
zbMATH Keywords: inverse problem
zbMATH Keywords: dissipative systems
zbMATH Keywords: Noether's theorem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3915686