Re: why an extra mark in legend?

• To: mathgroup at smc.vnet.net
• Subject: [mg106380] Re: [mg106240] why an extra mark in legend?
• From: Haibo Min <haibo.min at gmail.com>
• Date: Mon, 11 Jan 2010 05:29:26 -0500 (EST)
• References: <hi1qb7$ejb$1@smc.vnet.net> <201001070730.CAA23819@smc.vnet.net>

I am sorry that I didn't make it clear.

What I did is simulation using NDSolve. The code is as follows, and the
problem is that It was supposed to have three marks in the legend for \tau,
but I got four, where one of the marks had no text. Why?
Needs["PlotLegends"];
Subscript[m, 1] = 1; Subscript[l, 1] = 1; Subscript[m, e] = 2; \
Subscript[\[Delta], e] = \[Pi]/
6; Subscript[I, 1] = 0.12; Subscript[l, c1] = 0.5; Subscript[i, e] \
= 0.25; Subscript[l, ce] = 0.6;
K = 2; T = 1; \[CapitalGamma] =
2 IdentityMatrix[4]; \[CapitalLambda] = \[CapitalGamma]; B = 0.5;
a1 = Subscript[I, 1] + Subscript[m, 1] Subscript[l, c1]^2 + Subscript[
i, e] + Subscript[m, e] Subscript[l, ce]^2 +
Subscript[m, e] Subscript[l, 1]^2;
a2 = Subscript[i, e] + Subscript[m, e] Subscript[l, ce]^2;
a3 = Subscript[m, e] Subscript[l, 1] Subscript[l, ce]
Cos[Subscript[\[Delta], e]];
a4 = Subscript[m, e] Subscript[l, 1] Subscript[l, ce]
Sin[Subscript[\[Delta], e]];
qm[t1_] := {qm1[t1], qm2[t1]};
qmm[tm1_] := {qmm1[tm1], qmm2[tm1]};
qs[t3_] := {qs1[t3], qs2[t3]};
qss[tm3_] := {qss1[tm3], qss2[tm3]};
\[Epsilon]m[
t11_] := {-qm1'[t11] + qs1[t11 - T] - qm1[t11], -qm2'[t11] +
qs2[t11 - T] - qm2[t11]};
\[Epsilon]s[
t12_] := {-qs1'[t12] + qmm1[t12 - T] - qs1[t12], -qs2'[t12] +
qmm2[t12 - T] - qs2[t12]};
\[Epsilon]mm[
t13_] := {-qmm1'[t13] + qss1[t13 - T] - qmm1[t13], -qmm2'[t13] +
qss2[t13 - T] - qmm2[t13]}; \[Epsilon]ss[
t14_] := {-qss1'[t14] + qm1[t14 - T] - qss1[t14], -qss2'[t14] +
qm2[t14 - T] - qss2[t14]};
\[Tau]m[t15_] :=
K \[Epsilon]m[t15] + B (D[qs[t15 - T] - qm[t15], t15]);
\[Tau]s[t16_] :=
K \[Epsilon]s[t16] + B (D[qmm[t16 - T] - qs[t16], t16]); \[Tau]mm[
t17_] := K \[Epsilon]mm[t17] +
B (D[qss[t17 - T] - qmm[t17], t17]); \[Tau]ss[t18_] :=
K \[Epsilon]ss[t18] + B (D[qm[t18 - T] - qss[t18], t18]);
Hm11[t5_] := a1 + 2 a3 Cos[qm[t5][[2]]] + 2 a4 Sin[qm[t5][[2]]];
Hm12[t6_] := a2 + a3 Cos[qm[t6][[2]]] + a4 Sin[qm[t6][[2]]];
Hm21[t7_] := Hm12[t7];
Hm22 = a2;
hm[t9_] := a3 Sin[qm[t9][[2]]] - a4 Cos[qm[t9][[2]]];
Hmm11[tm5_] := a1 + 2 a3 Cos[qmm[tm5][[2]]] + 2 a4 Sin[qmm[tm5][[2]]];
Hmm12[tm6_] := a2 + a3 Cos[qmm[tm6][[2]]] + a4 Sin[qmm[tm6][[2]]];
Hmm21[tm7_] := Hmm12[tm7];
Hmm22 = a2;
hmm[tm9_] := a3 Sin[qmm[tm9][[2]]] - a4 Cos[qmm[tm9][[2]]];
Mm[t8_] := ( {
{Hm11[t8], Hm12[t8]},
{Hm12[t8], Hm22}
} );
Cm[t10_] := ( {
{-hm[t10] D[qm[t10][[2]],
t10], -hm[t10] (D[qm[t10][[2]], t10] + D[qm[t10][[1]], t10])},
{hm[t10] D[qm[t10][[1]], t10], 0}
} )
Mmm[tm8_] := ( {
{Hmm11[tm8], Hmm12[tm8]},
{Hmm12[tm8], Hmm22}
} );
Cmm[tm10_] := ( {
{-hmm[tm10] D[qmm[tm10][[2]],
tm10], -hmm[tm10] (D[qmm[tm10][[2]], tm10] +
D[qmm[tm10][[1]], tm10])},
{hmm[tm10] D[qmm[tm10][[1]], tm10], 0}
} )
Hs11[tt5_] := a1 + 2 a3 Cos[qs[tt5][[2]]] + 2 a4 Sin[qs[tt5][[2]]];
Hs12[tt6_] := a2 + a3 Cos[qs[tt6][[2]]] + a4 Sin[qs[tt6][[2]]];
Hs21[tt7_] := Hs12[tt7];
Hs22 = a2;
hs[tt9_] := a3 Sin[qs[tt9][[2]]] - a4 Cos[qs[tt9][[2]]];
Hss11[tts5_] :=
a1 + 2 a3 Cos[qss[tts5][[2]]] + 2 a4 Sin[qss[tts5][[2]]];
Hss12[tts6_] := a2 + a3 Cos[qss[tts6][[2]]] + a4 Sin[qss[tts6][[2]]];
Hss21[tts7_] := Hss12[tts7];
Hss22 = a2;
hss[tts9_] := a3 Sin[qss[tts9][[2]]] - a4 Cos[qss[tts9][[2]]];
Ms[tt8_] := ( {
{Hs11[tt8], Hs12[tt8]},
{Hs12[tt8], Hs22}
} ); Cs[tt10_] := ( {
{-hs[tt10] D[qs[tt10][[2]],
tt10], -hs[tt10] (D[qs[tt10][[2]], tt10] +
D[qs[tt10][[1]], tt10])},
{hs[tt10] D[qs[tt10][[1]], tt10], 0}
} )
Mss[tts8_] := ( {
{Hss11[tts8], Hss12[tts8]},
{Hss12[tts8], Hss22}
} ); Css[tts10_] := ( {
{-hss[tts10] D[qss[tts10][[2]],
tts10], -hss[tts10] (D[qss[tts10][[2]], tts10] +
D[qss[tts10][[1]], tts10])},
{hss[tts10] D[qss[tts10][[1]], tts10], 0}
} )
Ym[ttt_] := ( {
{D[qm[ttt][[1]], ttt],
D[qm[ttt][[2]],
ttt], (2 D[qm[ttt][[1]], ttt] + D[qm[ttt][[2]], ttt]) Cos[
qm[ttt][[2]]] - (D[qm[ttt][[2]], ttt] qm[ttt][[1]] +
D[qm[ttt][[1]], ttt] qm[ttt][[2]] +
D[qm[ttt][[2]], ttt] qm[ttt][[2]]) Sin[
qm[ttt][[2]]], (2 D[qm[ttt][[1]], ttt] +
D[qm[ttt][[2]], ttt]) Sin[
qm[ttt][[2]]] + (D[qm[ttt][[2]], ttt] qm[ttt][[1]] +
D[qm[ttt][[1]], ttt] qm[ttt][[2]] +
D[qm[ttt][[2]], ttt] qm[ttt][[2]]) Cos[qm[ttt][[2]]]},
{0, D[qm[ttt][[1]], ttt] + D[qm[ttt][[2]], ttt],
D[qm[ttt][[1]], ttt] Cos[qm[ttt][[2]]] +
D[qm[ttt][[1]], ttt] qm[ttt][[1]] Sin[
qm[ttt][[2]]], -D[qm[ttt][[1]], ttt] qm[ttt][[1]] Cos[
qm[ttt][[2]]] + D[qm[ttt][[1]], ttt] Sin[qm[ttt][[2]]]}
} )
Ymm[tttm_] := ( {
{D[qmm[tttm][[1]], tttm],
D[qmm[tttm][[2]],
tttm], (2 D[qmm[tttm][[1]], tttm] + D[qmm[tttm][[2]], tttm]) Cos[
qmm[tttm][[2]]] - (D[qmm[tttm][[2]], tttm] qmm[tttm][[1]] +
D[qmm[tttm][[1]], tttm] qmm[tttm][[2]] +
D[qmm[tttm][[2]], tttm] qmm[tttm][[2]]) Sin[
qmm[tttm][[2]]], (2 D[qmm[tttm][[1]], tttm] +
D[qmm[tttm][[2]], tttm]) Sin[
qmm[tttm][[2]]] + (D[qmm[tttm][[2]], tttm] qmm[tttm][[1]] +
D[qmm[tttm][[1]], tttm] qmm[tttm][[2]] +
D[qmm[tttm][[2]], tttm] qmm[tttm][[2]]) Cos[qmm[tttm][[2]]]},
{0, D[qmm[tttm][[1]], tttm] + D[qmm[tttm][[2]], tttm],
D[qmm[tttm][[1]], tttm] Cos[qmm[tttm][[2]]] +
D[qmm[tttm][[1]], tttm] qmm[tttm][[1]] Sin[
qmm[tttm][[2]]], -D[qmm[tttm][[1]], tttm] qmm[tttm][[1]] Cos[
qmm[tttm][[2]]] + D[qmm[tttm][[1]], tttm] Sin[qmm[tttm][[2]]]}
} )
Ys[tttt_] := ( {
{D[qs[tttt][[1]], tttt],
D[qs[tttt][[2]],
tttt], (2 D[qs[tttt][[1]], tttt] + D[qs[tttt][[2]], tttt]) Cos[
qs[tttt][[2]]] - (D[qs[tttt][[2]], tttt] qs[tttt][[1]] +
D[qs[tttt][[1]], tttt] qs[tttt][[2]] +
D[qs[tttt][[2]], tttt] qs[tttt][[2]]) Sin[
qs[tttt][[2]]], (2 D[qs[tttt][[1]], tttt] +
D[qs[tttt][[2]], tttt]) Sin[
qs[tttt][[2]]] + (D[qs[tttt][[2]], tttt] qs[tttt][[1]] +
D[qs[tttt][[1]], tttt] qs[tttt][[2]] +
D[qs[tttt][[2]], tttt] qs[tttt][[2]]) Cos[qs[tttt][[2]]]},
{0, D[qs[tttt][[1]], tttt] + D[qs[tttt][[2]], tttt],
D[qs[tttt][[1]], tttt] Cos[qs[tttt][[2]]] +
D[qs[tttt][[1]], tttt] qs[tttt][[1]] Sin[
qs[tttt][[2]]], -D[qs[tttt][[1]], tttt] qs[tttt][[1]] Cos[
qs[tttt][[2]]] + D[qs[tttt][[1]], tttt] Sin[qs[tttt][[2]]]}
} )
Yss[tttts_] := ( {
{D[qss[tttts][[1]], tttts],
D[qss[tttts][[2]],
tttts], (2 D[qss[tttts][[1]], tttts] +
D[qss[tttts][[2]], tttts]) Cos[
qss[tttts][[2]]] - (D[qss[tttts][[2]], tttts] qss[tttts][[1]] +
D[qss[tttts][[1]], tttts] qss[tttts][[2]] +
D[qss[tttts][[2]], tttts] qss[tttts][[2]]) Sin[
qss[tttts][[2]]], (2 D[qss[tttts][[1]], tttts] +
D[qss[tttts][[2]], tttts]) Sin[
qss[tttts][[2]]] + (D[qss[tttts][[2]], tttts] qss[tttts][[1]] +
D[qss[tttts][[1]], tttts] qss[tttts][[2]] +
D[qss[tttts][[2]], tttts] qss[tttts][[2]]) Cos[
qss[tttts][[2]]]},
{0, D[qss[tttts][[1]], tttts] + D[qss[tttts][[2]], tttts],
D[qss[tttts][[1]], tttts] Cos[qss[tttts][[2]]] +
D[qss[tttts][[1]], tttts] qss[tttts][[1]] Sin[
qss[tttts][[2]]], -D[qss[tttts][[1]], tttts] qss[tttts][[
1]] Cos[qss[tttts][[2]]] +
D[qss[tttts][[1]], tttts] Sin[qss[tttts][[2]]]}
} )
\[Theta]m[
time_] := {\[Theta]m1[time], \[Theta]m2[time], \[Theta]m3[
time], \[Theta]m4[time]};
\[Theta]mm[
timem_] := {\[Theta]mm1[timem], \[Theta]mm2[timem], \[Theta]mm3[
timem], \[Theta]mm4[timem]};
\[Theta]s[
time1_] := {\[Theta]s1[time1], \[Theta]s2[time1], \[Theta]s3[
time1], \[Theta]s4[time1]};
\[Theta]ss[
times1_] := {\[Theta]ss1[times1], \[Theta]ss2[times1], \[Theta]ss3[
times1], \[Theta]ss4[times1]};
s = NDSolve[{Mm[t][[1, 1]] \[Epsilon]m'[t][[1]] +
Mm[t][[1, 2]] \[Epsilon]m'[t][[2]] +
Cm[t][[1, 1]] \[Epsilon]m[t][[1]] +
Cm[t][[1, 2]] \[Epsilon]m[t][[2]] ==
Ym[t][[1, 1]] \[Theta]m[t][[1]] +
Ym[t][[1, 2]] \[Theta]m[t][[2]] +
Ym[t][[1, 3]] \[Theta]m[t][[3]] +
Ym[t][[1, 4]] \[Theta]m[t][[4]] - \[Tau]m[t][[1]],
Mm[t][[2, 1]] \[Epsilon]m'[t][[1]] +
Mm[t][[2, 2]] \[Epsilon]m'[t][[2]] +
Cm[t][[2, 1]] \[Epsilon]m[t][[1]] +
Cm[t][[2, 2]] \[Epsilon]m[t][[2]] ==
Ym[t][[2, 1]] \[Theta]m[t][[1]] +
Ym[t][[2, 2]] \[Theta]m[t][[2]] +
Ym[t][[2, 3]] \[Theta]m[t][[3]] +
Ym[t][[2, 4]] \[Theta]m[t][[4]] - \[Tau]m[t][[2]],
Mmm[t][[1, 1]] \[Epsilon]mm'[t][[1]] +
Mmm[t][[1, 2]] \[Epsilon]mm'[t][[2]] +
Cmm[t][[1, 1]] \[Epsilon]mm[t][[1]] +
Cmm[t][[1, 2]] \[Epsilon]mm[t][[2]] ==
Ymm[t][[1, 1]] \[Theta]mm[t][[1]] +
Ymm[t][[1, 2]] \[Theta]mm[t][[2]] +
Ymm[t][[1, 3]] \[Theta]mm[t][[3]] +
Ymm[t][[1, 4]] \[Theta]mm[t][[4]] - \[Tau]mm[t][[1]],
Mmm[t][[2, 1]] \[Epsilon]mm'[t][[1]] +
Mmm[t][[2, 2]] \[Epsilon]mm'[t][[2]] +
Cmm[t][[2, 1]] \[Epsilon]mm[t][[1]] +
Cmm[t][[2, 2]] \[Epsilon]mm[t][[2]] ==
Ymm[t][[2, 1]] \[Theta]mm[t][[1]] +
Ymm[t][[2, 2]] \[Theta]mm[t][[2]] +
Ymm[t][[2, 3]] \[Theta]mm[t][[3]] +
Ymm[t][[2, 4]] \[Theta]mm[t][[4]] - \[Tau]mm[t][[2]],
Ms[t][[1, 1]] \[Epsilon]s'[t][[1]] +
Ms[t][[1, 2]] \[Epsilon]s'[t][[2]] +
Cs[t][[1, 1]] \[Epsilon]s[t][[1]] +
Cs[t][[1, 2]] \[Epsilon]s[t][[2]] ==
Ys[t][[1, 1]] \[Theta]s[t][[1]] +
Ys[t][[1, 2]] \[Theta]s[t][[2]] +
Ys[t][[1, 3]] \[Theta]s[t][[3]] +
Ys[t][[1, 4]] \[Theta]s[t][[4]] - \[Tau]s[t][[1]],
Ms[t][[2, 1]] \[Epsilon]s'[t][[1]] +
Ms[t][[2, 2]] \[Epsilon]s'[t][[2]] +
Cs[t][[2, 1]] \[Epsilon]s[t][[1]] +
Cs[t][[2, 2]] \[Epsilon]s[t][[2]] ==
Ys[t][[2, 1]] \[Theta]s[t][[1]] +
Ys[t][[2, 2]] \[Theta]s[t][[2]] +
Ys[t][[2, 3]] \[Theta]s[t][[3]] +
Ys[t][[2, 4]] \[Theta]s[t][[4]] - \[Tau]s[t][[2]],
Mss[t][[1, 1]] \[Epsilon]ss'[t][[1]] +
Mss[t][[1, 2]] \[Epsilon]ss'[t][[2]] +
Css[t][[1, 1]] \[Epsilon]ss[t][[1]] +
Css[t][[1, 2]] \[Epsilon]ss[t][[2]] ==
Yss[t][[1, 1]] \[Theta]ss[t][[1]] +
Yss[t][[1, 2]] \[Theta]ss[t][[2]] +
Yss[t][[1, 3]] \[Theta]ss[t][[3]] +
Yss[t][[1, 4]] \[Theta]ss[t][[4]] - \[Tau]ss[t][[1]],
Mss[t][[2, 1]] \[Epsilon]ss'[t][[1]] +
Mss[t][[2, 2]] \[Epsilon]ss'[t][[2]] +
Css[t][[2, 1]] \[Epsilon]ss[t][[1]] +
Css[t][[2, 2]] \[Epsilon]ss[t][[2]] ==
Yss[t][[2, 1]] \[Theta]ss[t][[1]] +
Yss[t][[2, 2]] \[Theta]ss[t][[2]] +
Yss[t][[2, 3]] \[Theta]ss[t][[3]] +
Yss[t][[2, 4]] \[Theta]ss[t][[4]] - \[Tau]ss[t][[
2]], \[Theta]m'[t][[
1]] == -(Transpose[Ym[t]][[1, 1]] \[Epsilon]m[t][[1]] +
Transpose[Ym[t]][[1, 2]] \[Epsilon]m[t][[2]]), \[Theta]m'[t][[
2]] == -(Transpose[Ym[t]][[2, 1]] \[Epsilon]m[t][[1]] +
Transpose[Ym[t]][[2, 2]] \[Epsilon]m[t][[2]]), \[Theta]m'[t][[
3]] == -(Transpose[Ym[t]][[3, 1]] \[Epsilon]m[t][[1]] +
Transpose[Ym[t]][[3, 2]] \[Epsilon]m[t][[2]]), \[Theta]m'[t][[
4]] == -(Transpose[Ym[t]][[4, 1]] \[Epsilon]m[t][[1]] +
Transpose[Ym[t]][[4, 2]] \[Epsilon]m[t][[2]]), \[Theta]s'[t][[
1]] == -(Transpose[Ys[t]][[1, 1]] \[Epsilon]s[t][[1]] +
Transpose[Ys[t]][[1, 2]] \[Epsilon]s[t][[2]]), \[Theta]s'[t][[
2]] == -(Transpose[Ys[t]][[2, 1]] \[Epsilon]s[t][[1]] +
Transpose[Ys[t]][[2, 2]] \[Epsilon]s[t][[2]]), \[Theta]s'[t][[
3]] == -(Transpose[Ys[t]][[3, 1]] \[Epsilon]s[t][[1]] +
Transpose[Ys[t]][[3, 2]] \[Epsilon]s[t][[2]]), \[Theta]s'[t][[
4]] == -(Transpose[Ys[t]][[4, 1]] \[Epsilon]s[t][[1]] +
Transpose[Ys[t]][[4, 2]] \[Epsilon]s[t][[2]]), \[Theta]mm'[
t][[1]] == -(Transpose[Ymm[t]][[1, 1]] \[Epsilon]mm[t][[1]] +
Transpose[Ymm[t]][[1, 2]] \[Epsilon]mm[t][[2]]), \[Theta]mm'[
t][[2]] == -(Transpose[Ymm[t]][[2, 1]] \[Epsilon]mm[t][[1]] +
Transpose[Ymm[t]][[2, 2]] \[Epsilon]mm[t][[2]]), \[Theta]mm'[
t][[3]] == -(Transpose[Ymm[t]][[3, 1]] \[Epsilon]mm[t][[1]] +
Transpose[Ymm[t]][[3, 2]] \[Epsilon]mm[t][[2]]), \[Theta]mm'[
t][[4]] == -(Transpose[Ymm[t]][[4, 1]] \[Epsilon]mm[t][[1]] +
Transpose[Ymm[t]][[4, 2]] \[Epsilon]mm[t][[2]]), \[Theta]ss'[
t][[1]] == -(Transpose[Yss[t]][[1, 1]] \[Epsilon]ss[t][[1]] +
Transpose[Yss[t]][[1, 2]] \[Epsilon]ss[t][[2]]), \[Theta]ss'[
t][[2]] == -(Transpose[Yss[t]][[2, 1]] \[Epsilon]ss[t][[1]] +
Transpose[Yss[t]][[2, 2]] \[Epsilon]ss[t][[2]]), \[Theta]ss'[
t][[3]] == -(Transpose[Yss[t]][[3, 1]] \[Epsilon]ss[t][[1]] +
Transpose[Yss[t]][[3, 2]] \[Epsilon]ss[t][[2]]), \[Theta]ss'[
t][[4]] == -(Transpose[Yss[t]][[4, 1]] \[Epsilon]ss[t][[1]] +
Transpose[Yss[t]][[4, 2]] \[Epsilon]ss[t][[2]]),
qmm1[t /; t <= 0] == 0.2, qmm1'[t /; t <= 0] == -0.15,
qmm2[t /; t <= 0] == 0.1, qmm2'[t /; t <= 0] == 0.1,
qss1[t /; t <= 0] == 0.1, qss1'[t /; t <= 0] == 0.1,
qss2[t /; t <= 0] == -0.1,
qss2'[t /; t <= 0] == 0.3, \[Theta]mm1[t /; t <= 0] ==
0.8 a1, \[Theta]mm2[t /; t <= 0] ==
0.8 a2, \[Theta]mm3[t /; t <= 0] ==
0.8 a3, \[Theta]mm4[t /; t <= 0] ==
0.1, \[Theta]ss1[t /; t <= 0] ==
0.8 a1, \[Theta]ss2[t /; t <= 0] ==
0.8 a2, \[Theta]ss3[t /; t <= 0] ==
0.8 a3, \[Theta]ss4[t /; t <= 0] == 0.8 a4,
qm1[t /; t <= 0] == -0.1, qm1'[t /; t <= 0] == -0.2,
qm2[t /; t <= 0] == 0.1, qm2'[t /; t <= 0] == 0.1,
qs1[t /; t <= 0] == -0.3, qs1'[t /; t <= 0] == 0.2,
qs2[t /; t <= 0] == -0.2,
qs2'[t /; t <= 0] == 0.1, \[Theta]m1[t /; t <= 0] ==
0.8 a1, \[Theta]m2[t /; t <= 0] ==
0.8 a2, \[Theta]m3[t /; t <= 0] ==
0.8 a3, \[Theta]m4[t /; t <= 0] ==
0.8 a4, \[Theta]s1[t /; t <= 0] ==
0.8 a1, \[Theta]s2[t /; t <= 0] ==
0.8 a2, \[Theta]s3[t /; t <= 0] ==
0.8 a3, \[Theta]s4[t /; t <= 0] == 0.8 a4}, {qmm1, qmm2, qss1,
qss2, \[Theta]mm1, \[Theta]mm2, \[Theta]mm3, \[Theta]mm4, \
\[Theta]ss1, \[Theta]ss2, \[Theta]ss3, \[Theta]ss4, qm1, qm2, qs1,
qs2, \[Theta]m1, \[Theta]m2, \[Theta]m3, \[Theta]m4, \[Theta]s1, \
\[Theta]s2, \[Theta]s3, \[Theta]s4}, {t, 0, 100}];
GraphicsRow[{Plot[{\[Tau]s[t][[1]], \[Tau]ss[t][[1]], \[Tau]mm[
t][[1]]} /. s // Evaluate, {t, 0, 20},
PlotRange -> {{0, 20}, {-2, 1}}, Frame -> True, Axes -> True,
FrameLabel -> {"Time(s)",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"i\", RowBox[{\"(\", \"1\", \")\"}]]$$'(t)"},
PlotStyle -> {{Red, Dashed, Thick}, {Blue, Thick}, {Black, Dotted,
Thick}},
PlotLegend -> {"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"2\", RowBox[{\"(\", \"1\", \")\"}]]$$",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"3\", RowBox[{\"(\", \"1\", \")\"}]]$$",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"4\", RowBox[{\"(\", \"1\", \")\"}]]$$"}, LegendPosition -> {0.5, -0.3},
LegendSize -> {0.2, 0.3}, LegendShadow -> None],
Plot[{\[Tau]s[t][[2]], \[Tau]ss[t][[2]], \[Tau]mm[t][[2]]} /. s //
Evaluate, {t, 0, 20}, PlotRange -> {{0, 20}, {-1, 2}},
Frame -> True, Axes -> True,
FrameLabel -> {"Time(s)",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"i\", RowBox[{\"(\", \"2\", \")\"}]]$$'(t)"},
PlotStyle -> {{Red, Dashed, Thick}, {Blue, Thick}, {Black, Dotted,
Thick}},
PlotLegend -> {"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"2\", RowBox[{\"(\", \"2\", \")\"}]]$$",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"3\", RowBox[{\"(\", \"2\", \")\"}]]$$",
"\!$$\*SubsuperscriptBox[\"\[Tau]\", \"4\", RowBox[{\"(\", \"2\", \")\"}]]$$"}, LegendPosition -> {0.5, 0.1},
LegendSize -> {0.2, 0.3}, LegendShadow -> None,
ImageSize -> {450, 300}]}, ImageSize -> {900, 300}, Spacings -> 0]

`

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