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| <math>\begin{align} | | <math>\begin{align} |
| & \delta S\left[ q \right]=\cancel {\left[ {{\partial }_{{\dot{q}}}}L\delta q \right]_{{{t}_{1}}}^{{{t}_{2}}}} -\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{\partial }_{q}}L\delta q-{{d}_{t}}\left( {{\partial }_{{\dot{q}}}}L \right)\delta q \right)dt} \\
| | \delta S\left[ q \right]=- \cancel {\left[ {{\partial }_{{\dot{q}}}}L\delta q \right]_{{{t}_{1}}}^{{{t}_{2}}}} -\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{\partial }_{q}}L\delta q-{{d}_{t}}\left( {{\partial }_{{\dot{q}}}}L \right)\delta q \right)dt} \\ |
| & =\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L\delta qdt} | | & =\int\limits_{{{t}_{1}}}^{{{t}_{2}}}{\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L\delta qdt} |
| \end{align}</math> | | \end{align}</math> |
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| <math>\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L=0</math> | | <math>\left( {{d}_{t}}{{\partial }_{{\dot{q}}}}-{{\partial }_{q}} \right)L=0</math> |
| | | [[FragenID:M2]] |
| [[Kategorie:Mechanik]] | | [[Kategorie:Mechanik]] |
auch Prinzip der kleinsten Wirkung genannt
mit
spezielle Form
führt zur Wirkung
FragenID::M1
Herleitung der Euler-Lagrange-Gleichungen
oder
mit partieller Integration () mit
FragenID:M2
Kategorie:Mechanik