ClearAll["Global`*"];

y1 := L1 Cos[ϕ1[t]] ; 
x1 := L1 Sin[ϕ1[t]] ; 
y2 := y1 + L2 Cos[ϕ2[t]] ; 
x2 := x1 + L2 Sin[ϕ2[t]];
x1dot := D[x1, t];
y1dot := D[y1, t];
x2dot := D[x2, t];
y2dot := D[y2, t];
T := (m1/2) (x1dot^2 + y1dot^2) + (m2/2) (x2dot^2 + y2dot^2)
FullSimplify[T]

(* note that I defined y axis to point downward *)
U := -m1 g y1 - m2 g y2
L := T-U
FullSimplify[L]

eomexpr1 := D[D[L,ϕ1'[t]], t] == D[L, ϕ1[t]]
eom1 := FullSimplify[eomexpr1]
eom1

eomexpr2 := D[D[L,ϕ2'[t]], t] == D[L, ϕ2[t]]
eom2 :=FullSimplify[eomexpr2]
eom2

L1 = 1 ; L2 = 1 ; m1 = 1 ; m2 = 1; g = 9.8; 
a = 0.1; b = -Sqrt[2]; tmax = 10;
soln=NDSolve[
{eom1, eom2, 
ϕ1'[0]==0, ϕ2'[0]==0, 
ϕ1[0] == a, ϕ2[0] == a b},
{ϕ1[t], ϕ2[t]},
{t, 0, tmax}];
phi1[t_] := Evaluate[ϕ1[t] /. First[soln]]
phi2[t_] := Evaluate[ϕ2[t] /. First[soln]]
Plot[{phi1[t], phi2[t]}, {t, 0, tmax}]

xx1[t_] := L1 Sin[phi1[t]];
yy1[t_] := -L1 Cos[phi1[t]];
xx2[t_] := xx1[t]+L1 Sin[phi2[t]];
yy2[t_] := yy1[t]-L2 Cos[phi2[t]];
bobradius = 0.03;
Manipulate[
L1 = 1 ; L2 = 1 ; m1 = 1 ; m2 = 1; g = 9.8; 
soln=NDSolve[
{eom1, eom2, 
ϕ1'[0]==0, ϕ2'[0]==0, 
ϕ1[0] == a, ϕ2[0] == a b},
{ϕ1[t], ϕ2[t]},
{t, 0, tmax}];
phi1[t_] := Evaluate[ϕ1[t] /. First[soln]];
phi2[t_] := Evaluate[ϕ2[t] /. First[soln]];
Animate[
Graphics[
{
Line[{{0,0}, {xx1[t], yy1[t]}}],
Disk[{xx1[t], yy1[t]}, bobradius],
Line[{{xx1[t], yy1[t]}, {xx2[t], yy2[t]}}],
Disk[{xx2[t], yy2[t]}, bobradius]
},
Axes->True, PlotRange->{{-2, 2}, {2, -2}}
], {t, 0, tmax}],
{{a, 0.1}, -1.5, 1.5},
{{b, Sqrt[2]}, -Sqrt[2], +Sqrt[2]},
{{tmax, 10}, 0, 100}]

Manipulate[
L1 = 1 ; L2 = 1 ; m1 = 1 ; m2 = 1; g = 9.8; 
soln=NDSolve[
{eom1, eom2, 
ϕ1'[0]==0, ϕ2'[0]==0, 
ϕ1[0] == a, ϕ2[0] == a b},
{ϕ1[t], ϕ2[t]},
{t, 0, tmax}];
phi1[t_] := Evaluate[ϕ1[t] /. First[soln]];
phi2[t_] := Evaluate[ϕ2[t] /. First[soln]];
Plot[{phi1[t], phi2[t]}, {t, 0, tmax}],
{{a, 0.1}, -1.5, 1.5},
{{b, Sqrt[2]}, -Sqrt[2], +Sqrt[2]},
{{tmax, 10}, 0, 100}]

ClearAll["Global`*"];
m = {{a, b, c}, {d, e, f}, {g, h, i}};
MatrixForm[m]
Det[m]