Generalization of Noether’s theorem for systems with variable mass

Djordje Mušicki

Theoretical and applied mechanics, Tome 23 (1997) no. 1, p. 129 .

Résumé

In this article it is demonstrated that the generalization of Noether’s theorem to the systems with variable mass can be effectuated directly, starting form the total variation of action, which here has one additional specific term and employing the corresponding Lagrangian equations. In this manner the direct Noether’s theorem for such systems is obtained in a more general form, which represents a certain generalization of this obtained by L. Cveticanin in indirect way from d’Alembert-Lagrange’s principle. In addition, the corresponding generalized Killing’s equations and the inverse Noether’s theorem are formulated, including the generate systems also. The found results are illustrated by a simple, but characteristic example.