Needs["VariationalMethods`"]
ClearAll[Global]


variables = {Subscript[[Theta], 1][t], Subscript[[Theta], 2][t],
   Subscript[[Theta], 3][t]};
Subscript[r, 1] =
  Subscript[l,
   1] {Sin[Subscript[[Theta], 1][t]], -Cos[
      Subscript[[Theta], 1][t]]};
Subscript[r, 2] =
  Subscript[r, 1] +
   Subscript[l,
    2] {Sin[Subscript[[Theta], 2][t]], -Cos[
       Subscript[[Theta], 2][t]]};
Subscript[r, 3] =
  Subscript[r, 2] +
   Subscript[l,
    3] {Sin[Subscript[[Theta], 3][t]], -Cos[
       Subscript[[Theta], 3][t]]};

Subscript[l, 1] = 1;
Subscript[l, 2] = 1;
Subscript[l, 3] = 1;
Subscript[m, 1] = 1;
Subscript[m, 2] = 1;
Subscript[m, 3] = 1;
g = 9.81;
tMax = 10;
initial = {Subscript[[Theta], 1][0] == Pi/2,
   Subscript[[Theta], 2][0] == Pi, Subscript[[Theta], 3][0] == Pi/2,
    Subscript[[Theta], 1]'[0] == Pi/2,
   Subscript[[Theta], 2]'[0] == 0, Subscript[[Theta], 3]'[0] == 0};


lagrangian = (Subscript[m, 1]/2) D[Subscript[r, 1], t].D[Subscript[r,
      1], t] + (Subscript[m, 2]/2) D[Subscript[r, 2], t].D[Subscript[
      r, 2], t] + (Subscript[m, 3]/2) D[Subscript[r, 3], t].D[
      Subscript[r, 3], t] -
   g {0, 1}.(Subscript[m, 1]*Subscript[r, 1] +
       Subscript[m, 2]*Subscript[r, 2] +
       Subscript[m, 3]*Subscript[r, 3]);
eqs = EulerEquations[lagrangian, variables, t];

sol = First[NDSolve[Join[eqs, initial], variables, {t, 0, tMax}]];

Plot[Subscript[[Theta], 2]'[t] /. sol, {t, 0, 10}]