摘要Conservation laws for partially conservative variable mass dynamical systems under symmetric infinitesimal transformations are determined. A generalization of Lagrange--d'Alembert's principle for a variable mass system in terms of asynchronous virtual variation is presented. The generalized Killing equations are obtained such that their solution yields the transformations and the associated conservation laws. An example illustrative of the theory is furnished at the end as well.
Abstract:Conservation laws for partially conservative variable mass dynamical systems under symmetric infinitesimal transformations are determined. A generalization of Lagrange--d'Alembert's principle for a variable mass system in terms of asynchronous virtual variation is presented. The generalized Killing equations are obtained such that their solution yields the transformations and the associated conservation laws. An example illustrative of the theory is furnished at the end as well.
[1] Luo S K 1994 Appl. Math. Mech. 15 147 [2] Fang J H and Zhao S Q 2002 Chin. Phys. 11445 [3] Qiao Y F, Li R J and Zhao S H 2004 Chin. Phys. 11 1790 [4] Li R J, Qiao Y F and Liu Y 2002 Chin. Phys. 11 760 [5] Mei F X 1999 Appl. Math. Mech. 20 629 [6] Noether A E 1918 Nachr. Akad. Wiss. Gottingen Math.Phys. K$\!$I \& I$\!$I 235 [7] Vujanovic B 1978 Int. J. Non-Linear Mech. 13185 [8] Munawar H 1991 Lagrange Equations of Motion(Islamabad: University Grants Commission) chap 2 p 37 [9] Pars L A 1968 A Treatise on Analytical Dynamics(London: Heinemann) chap 11 p 190 [10] Bahar L Y and Kwatny H G 1987 Int. J. Non-LinearMech. 22 125 [11] Liu D 1989 Acta Mech. Sin. 5 167