Quantum redactiones paginae "Aequationes Lagrangi" differant

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Linea 14:
:::<math> \frac{\delta S}{\delta x_\alpha} = 0</math>.
 
EQua quoex aequatione Langrange obtinuitdeduxit aequationes Euler-Lagrange:
 
:::<math>\frac{d~}{dt} \ \left( \, \frac{\partial L}{\partial \dot{x}_\alpha} \, \right) \ - \ \frac{\partial L}{\partial x_\alpha} \ = \ 0</math>
 
Langrange deinde invenit has aequationes illi Newtonianae corrrespondere si solum si ''L = T - V'' ponamus, id est, si functio Lagrangiana ponatur aequalis differentiae inter energiam cineticam et energiam potentialem. Si singula particula [[Relativitas specialis|arelativistica]] energia ''V'' potentiali in tribus dimensionibus habeamus, functio Langrangiana sua est
 
:::<math>L(\vec{x}, \dot{\vec{x}}) \ = \ \frac{1}{2} \ m \ \dot{\vec{x}}^2 \ - \ V(\vec{x})</math>.
Linea 29:
:::<math>\frac{d~}{dt} \ \left( \, \frac{\partial L}{\partial \dot{x}_\alpha} \, \right) \ = \ m \, \ddot{x}_\alpha, </math>
 
ut possemus aequationes Euler-Lagrange scribere:
 
:::<math>m\ddot{\vec{x}}+\nabla V=0</math>.