Parameterdarstellung

Kurve in Parameterdarstellung:

	x(t)=1257-324 t+(-1304+684 t-57 (t^2)) cos(t)+47cos(2 t)+(-418-273t+62 (t^2)) sin(t)+16 sin(2 t)
	y(t)=-848+224 t+(864-452 t+36 (t^2)) cos(t)-16 cos(2 t)+(337 +138 t-38 (t^2)) sin(t)+4 sin(2 t)

für  0≤t≤7.4

Graphen der Funktionen t->x(t) und t->y(t)

Plot[
{1257-324 t+(-1304+684 t-57 (t^2)) Cos[t]+47Cos[2 t]+(-418-273t+62 (t^2)) Sin[t]+16 Sin[2 t],
-848+224 t+(864-452 t+36 (t^2)) Cos[t]-16 Cos[2 t]+(337 +138 t-38 (t^2)) Sin[t]+4 Sin[2 t]},
{t,0,7.4},PlotStyle->{Red,Blue},ImageSize->400]

Die Kurve t->(x(t),y(t))

ParametricPlot[
{1257-324 t+(-1304+684 t-57 (t^2)) Cos[t]+47Cos[2 t]+(-418-273t+62 (t^2)) Sin[t]+16 Sin[2 t],
-848+224 t+(864-452 t+36 (t^2)) Cos[t]-16 Cos[2 t]+(337 +138 t-38 (t^2)) Sin[t]+4 Sin[2 t]},
{t,0,7.4},PlotStyle->{Red,Thick},AxesStyle->Gray,PlotRange->{{-45,45},{-59,105}}]

Abhängigkeit der Kurve von den Koeffizienten

Column[{achsen=False;,
Manipulate[ParametricPlot[
{c0-c1 t+(-c2+c3 t-c4 (t^2)) Cos[t]+c5 Cos[2 t]+(-c6-c7 t+c8 (t^2)) Sin[t]+c9 Sin[2 t],
-d0+d1 t+(d2-d3 t+d4 (t^2)) Cos[t]-d5 Cos[2 t]+(d6 +d7 t-d8 (t^2)) Sin[t]+d9 Sin[2 t]},
{t,0,7.4},PlotStyle->{Red,Thick},Axes->achsen,AxesStyle->Gray],
{{c0,1257},1207,1307,Appearance->"Labeled"},
{{c1,324},322,326,Appearance->"Labeled"},
{{c2,1304},1298,1310,Appearance->"Labeled"},
{{c3,684},680,688,Appearance->"Labeled"},
{{c4,57},55,59,Appearance->"Labeled"},
{{c5,47},40,54,Appearance->"Labeled"},
{{c6,418},410,426,Appearance->"Labeled"},
{{c7,273},271,275,Appearance->"Labeled"},
{{c8,62},60,64,Appearance->"Labeled"},
{{c9,16},10,22,Appearance->"Labeled"},
{{d0,848},800,896,Appearance->"Labeled"},
{{d1,224},221,227,Appearance->"Labeled"},
{{d2,864},858,870,Appearance->"Labeled"},
{{d3,452},449,455,Appearance->"Labeled"},
{{d4,36},34,38,Appearance->"Labeled"},
{{d5,16},4,28,Appearance->"Labeled"},
{{d6,337},324,350,Appearance->"Labeled"},
{{d7,138},130,146,Appearance->"Labeled"},
{{d8,38},36,40,Appearance->"Labeled"},
{{d9,4},-2,10,Appearance->"Labeled"}],
Row[{"Achsen: ",Checkbox[Dynamic[achsen]]}]}]

Der Punkt (x(t),y(t)) für konkrete Werte von t

(* Position von (x(t),y(t)) in der xy-Ebene *)
Manipulate[
Row[{Graphics[{PointSize[0.025],Red,Point[
{1257-324 t+(-1304+684 t-57 (t^2)) Cos[t]+47Cos[2 t]+(-418-273t+62 (t^2)) Sin[t]+16 Sin[2 t],
-848+224 t+(864-452 t+36 (t^2)) Cos[t]-16 Cos[2 t]+(337 +138 t-38 (t^2)) Sin[t]+4 Sin[2 t]}
]},Axes->True,PlotRange->{{-45,45},{-59,105}},ImageSize->250],
Column[{
Row[{"   x(",t,") = ",1257-324 t+(-1304+684 t-57 (t^2)) Cos[t]+47Cos[2 t]+(-418-273t+62 (t^2)) Sin[t]+16 Sin[2 t]}],
Row[{"   y(",t,") = ",-848+224 t+(864-452 t+36 (t^2)) Cos[t]-16 Cos[2 t]+(337 +138 t-38 (t^2)) Sin[t]+4 Sin[2 t]}]}
]}],
{t,0,7.4,Appearance->"Labeled"}]

Kurvenstück zum Parameterintervall 0.01≤t≤tmax

(* Wert des Parameters t zwischen zwischen 0.01 und tmax *)
Manipulate[ParametricPlot[
{1257-324 t+(-1304+684 t-57 (t^2)) Cos[t]+47Cos[2 t]+(-418-273t+62 (t^2)) Sin[t]+16 Sin[2 t],
-848+224 t+(864-452 t+36 (t^2)) Cos[t]-16 Cos[2 t]+(337 +138 t-38 (t^2)) Sin[t]+4 Sin[2 t]},
{t,0,tmax},PlotStyle->{Red,Thick},AxesStyle->Gray,PlotRange->{{-45,45},{-59,105}}],{tmax,0.01,7.4,Appearance->"Labeled"}]