Formulació Lagrangiana. Tir Parabòlic Ingredients (font) Lagrangiana `L = E_c-E_p = 1/2m(\dotx^2+\doty^2)-mgy` Equacions Euler-lagrange `d/dt((\delta L)/(\delta \dotx))-(\delta L)/(\delta x)=0` `d/dt((\delta L)/(\delta \doty))-(\delta L)/(\delta y)=0` Càlculs Coordenada x `d/dt((\delta (1/2m(\dotx^2+\doty^2)-mgy))/(\delta \dotx))-(\delta (1/2m(\dotx^2+\doty^2)-mgy))/(\delta x)=0` `d/dt(1/2m2\dotx)=(d(m\dotx))/dt=m\ddotx=0` `\dotx=v_(x_0) => x=v_(x_0)t+e_(x_0)` Coordenada y `d/dt((\delta (1/2m(\dotx^2+\doty^2)-mgy))/(\delta \doty))-(\delta (1/2m(\dotx^2+\doty^2)-mgy))/(\delta y)=0` `d/dt(1/2m2\doty)+mg=(d(m\doty))/dt=m\ddoty+mg=0 => \ddoty+g=0 => \ddoty=-g` `\doty= -g t+v_(y_o) => y=-1/2g t^2+v_(y_o)t+e_(y_0)`