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The Symmetries of Equivalent Lagrangian Systems and Constants of Motion | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 7، دوره 22، شماره 1، خرداد 2011، صفحه 63-132 اصل مقاله (270.03 K) | ||
| نویسنده | ||
| N. Elyasi | ||
| Amirkabir University of Technology | ||
| چکیده | ||
| In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the case of time-dependent Lagrangian systems. Also some new theorems and corollaries will be proved. Finally we make a 1-1 correspondence between the symmetries of equivalent time-dependent lagrangian systems and constants of motion by the new geometric concept of Galilean space-time. | ||
| کلیدواژه‌ها | ||
| Infinitesimal symmetries؛ Lagrangian system؛ Symmetries of Lagrangian systems؛ Hamiltonian system؛ Constant of motion | ||
| عنوان مقاله [English] | ||
| The Symmetries of Equivalent Lagrangian Systems and Constants of Motion | ||
| نویسندگان [English] | ||
| N. Elyasi | ||
| چکیده [English] | ||
| In this paper Mathematical structure of time-dependent Lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent Lagrangian systems are considered. Starting point is time-independent Lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the case of time-dependent Lagrangian systems. Also some new theorems and corollaries will be proved. Finally we make a 1-1 correspondence between the symmetries of equivalent time-dependent lagrangian systems and constants of motion by the new geometric concept of Galilean space-time. | ||
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