<< VariationalMethods`
tmax = 1000;
solution = Block[{m, g, \[Theta], L, x, y, v, t},
   x = Accumulate[ 
     Sin[{Subscript[\[Theta], 1], Subscript[\[Theta], 2]}]];
   y = Accumulate[ -Cos[{Subscript[\[Theta], 1], Subscript[\[Theta], 
        2]}]];
   v = D[{x, y} /. 
      Subscript[\[Theta], i_] :> Subscript[\[Theta], i][t], t];
   L = Plus @@ (1/
        2 Map[# . # &, Transpose[v]] - (y /. 
         Subscript[\[Theta], i_] :> Subscript[\[Theta], i][t]));
   NDSolve[Join[Simplify[
      Table[
       EulerEquations[L, Subscript[\[Theta], i][t], t], {i, 1, 2}
       ]
      ], {Subscript[\[Theta], 1][0] == 22/7, 
      Subscript[\[Theta], 2][0] == 22/7, 
      Subscript[\[Theta], 1]'[0] == Subscript[\[Theta], 2]'[0] == 
       0}], {Subscript[\[Theta], 1], Subscript[\[Theta], 2]}, {t, 0, 
     tmax}]
   ];
ParametricPlot[
 Table[Subscript[\[Theta], i][t], {i, 2}] /. solution, {t, 0, tmax}]