A study of conservation laws of dynamical systems by means of the differential variational principles of Jourdain and Gauss
The author shows that the differential variational principles of Jourdain and Gauss can be employed as a starting point for the study of conservation laws of conservative and nonconservative systems with a finite number of degrees of freedom. He demonstrates that the introduction of the generalized (nonsimultaneous) variations in the sense of Jourdain and Gauss yields a Noether's-type theory for finding conservation laws. For the case of conservative systems, the outcome is identical with the classical Noether-theory. As a characteristic feature of the theory, the condition of the invariance of the Gauss constraint with respect to the infinitesimal transformations of the acceleration vector (including the time deformation) produces the condition for the existence of a conserved quantity (the basic Noether identity and corresponding conservation laws. Generally, it is difficult to select appropriate functions appearing in a basic identity.
differential variational principles of Jourdain
scientific article; zbMATH DE number 3990934