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Jun 21, 2020 at 1:06 comment added TaeNyFan @pasabaporaqui You did not express kinetic energy as $T={1\over 2}mv^2={1\over 2}m(\dot{x}^2+\dot{y}^2)$
Jun 13, 2020 at 18:11 comment added pasaba por aqui Thanks for your answer. Using "y" as generalized coordinate, $T(y)=T_0+mg(y_0-y)$, but method still fails. Do you mean I must express $T$ as a function of only $\dot{y}$? That seems to limit the method. Moreover, Lagrange equations could then be simplified using $\frac{\partial L}{\partial y}=\frac{\partial V}{\partial y}$ and $\frac{\partial L}{\partial \dot{y}}=\frac{\partial T}{\partial \dot{y}}$
Jun 13, 2020 at 6:23 history edited TaeNyFan CC BY-SA 4.0
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Jun 13, 2020 at 6:17 history answered TaeNyFan CC BY-SA 4.0