Lagrange’s equation

By combining the potential energy part and the kinetic energy part, we obtain the resulting Lagrange’s equation:

ml2N−1∑j=0{N−max(i,j)}dωjdtcos(θi−θj)+ml2N−1∑j=0{N−max(i,j)}ωjωjsin(θi−θj)−mgl(N−i)cosθi=0i.