Abstract
In this report we consider the possibility of using the differential variational principles of Jourdain and Gauss as a starting point for the study of conservation laws of holonomic conservative and nonconservative dynamical systems with a finite number of degrees of freedom. We demonstrate that this approach has the same status as the method based on the D'Alembert's differential variational principle developed in a previous paper.
Highlights
It is generally accepted that the conservation laws of the classical dynamical systems are always of mathematical importance and at the same time, they are regarded as the manifestation of some profound physical principle.In general, there are a variety of approaches to take in finding conservation laws
It is demonstrated that the introduction of the generalized variations in the sense of Jourdain and Gauss, a Noether's-type theory for finding conservation laws can be established
For the case of purely conservative dynamical systems, the outcome is identical with the classical Noether's theory obtained by means of the Hamilton's principle
Summary
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A Study of Conservation Laws of Dynamical Systems by Means of the Differential Variational Principles of Jourdain and Gauss*
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