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equations:euler_lagrange_equations [2018/03/27 09:11] jakobadmin [Concrete] |
equations:euler_lagrange_equations [2018/03/28 10:22] jakobadmin |
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- | ====== Euler-Lagrange Equations: $\quad \frac{\partial \mathscr{L}}{\partial \Phi^i} - \partial_\mu \left(\frac{\partial \mathscr{L}}{\partial(\partial_\mu\Phi^i)}\right) = 0 $ ====== | + | <WRAP lag>$ \frac{\partial \mathscr{L}}{\partial \Phi^i} - \partial_\mu \left(\frac{\partial \mathscr{L}}{\partial(\partial_\mu\Phi^i)}\right) = 0 $</WRAP> |
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+ | ====== Euler-Lagrange Equations ====== | ||
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- | $$ \text{For particles: } \frac{\partial L}{\partial q_i} - \frac{d }{d t}\frac{\partial L}{\partial \dot{q_i}} = 0 \qquad \text{For fields: } \frac{\partial \mathscr{L}}{\partial \Phi^i} - \partial_\mu \left(\frac{\partial \mathscr{L}}{\partial(\partial_\mu\Phi^i)}\right) = 0 $$ | + | $$ \text{For particles: } \frac{\partial L}{\partial q_i} - \frac{d }{d t}\frac{\partial L}{\partial \dot{q_i}} = 0 . $$ |
The Euler-Lagrange equation can also be used in a field theory and there it tells us which sequence of field configurations has minimal action. | The Euler-Lagrange equation can also be used in a field theory and there it tells us which sequence of field configurations has minimal action. |