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Ndsolve solution cant manipulate parametric plot!!

 ClearAll[x, y, θ];
 L = 1;

v1[t_] := 5 UnitStep[t - 10] - 5 UnitStep[t - 30];
v2[t_] := 4 UnitStep[t - 20] - 4 UnitStep[t - 50];
v3[t_] := 6 UnitStep[t - 50] - 6 UnitStep[t - 80];

eq1 = -2/3*Sin[θ[t]]*v1[t] - 
    2/3*Sin[Pi/3 - θ[t]]*v2[t] + 
    2/3*Sin[Pi/3 + θ[t]]*v3[t] - x'[t] == 0;
eq2 = 2/3*Cos[θ[t]]*v1[t] - 
    2/3*Cos[Pi/3 - θ[t]]*v2[t] - 
    2/3*Cos[Pi/3 + θ[t]]*v3[t] - y'[t] == 0;
eq3 = 1/3 L*(v1[t] + v2[t] + v3[t]) - θ'[t] == 0;
ics = {x[0] == 1, y[0] == 0, θ[0] == 0};
eqs = Join[{eq1, eq2, eq3}, ics];

sol = First@NDSolve[eqs, {x[t], y[t], θ[t]}, {t, 0, 100}];
Plot[Evaluate[{x[t], y[t], θ[t]} /. sol], {t, 0, 100}, 
     PlotStyle -> {{Thick, Red}, {Thick, Blue, Dashed}, {Thick, Black,  Dotted}}]

Manipulate[
 Graphics[Rotate[
   Rectangle[{Evaluate[{x[a]} /. sol], Evaluate[{y[a]} /. sol]}], 
   Evaluate[{θ[a]} /. sol]]], {a, 0.1, 100}]
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  • $\begingroup$ One possibility: Replace {x[t], y[t], θ[t]} with {x, y, θ} in NDSolve, and get rid of the {}'s surrounding x[a], y[a], and θ[a] in your Manipulate expression. $\endgroup$
    – march
    Jul 16, 2015 at 20:44

1 Answer 1

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Perhaps you want something like:

sol = First@NDSolve[eqs, {x, y, θ}, {t, 0, 100}];
Manipulate[Graphics[Rotate[Rectangle[{0, 0}, {y[a], x[a]}], θ[a]] /. sol,
                    Axes -> True], {a, 0.1, 100}]

Mathematica graphics

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