Animation of parametric curves which includes Osculating Plane, Circle, Sphere, and Planetary motion visualization.
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Animate[Plot[Sin[ωx],{ω,1,30}],{x,0,2Pi},AnimationRunning->False]
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Plot3D[x^2+y^2,{x,2,9},{y,-4,8}]
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Animate[Plot3D[x^2+y^2,{x,2,9},{y,-4,8}],{t,0,1},AnimationRunning->False]
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Animate[ParametricPlot[{rCos[t],rSin[t]},{t,0,2Pi}],{r,0,1},AnimationRunning->False]
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curve={Cos[t],Sin[t],t};Animate[Show[ParametricPlot3D[curve,{t,0,2Pi},PlotStyle->{Thick,Blue}],Graphics3D[{Opacity[0.5],EdgeForm[],FaceForm[Yellow],InfinitePlane[curve/.t->t0,{t,t0-0.5,t0+0.5}]}]],{t0,0,2Pi},AnimationRunning->False]
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curve={t,t^2};Animate[Show[ParametricPlot[curve,{t,-2,2},PlotRange->{{-2,2},{-2,4}}],Graphics[{Red,Circle[curve/.t->t0,1/Norm[curve/.t->t0]]}]],{t0,-2,2},AnimationRunning->False]
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curve={t,Sin[t],Cos[t]};Animate[Show[ParametricPlot3D[curve,{t,0,2Pi},PlotStyle->{Thick,Blue}],Graphics3D[{Opacity[0.5],EdgeForm[],FaceForm[Yellow],Sphere[curve/.t->t0,0.2]}]],{t0,0,2Pi},AnimationRunning->False]
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G=6.67430*10^-11;(*gravitationalconstant*)M=5.97219*10^24;(*massofthecentralbody(e.g.,Earth)*)(*Parametersfortheplanetarymotion*)a=1;(*semi-majoraxis*)b=0.8;(*semi-minoraxis*)T=10;(*periodofrevolution*)theta=0;(*initialangle*)(*Functiontocomputethepositionoftheplanetatagiventime*)position[t_]:={aCos[2Pit/T+theta],bSin[2Pit/T+theta]};Animate[ParametricPlot[position[t],{t,0,T},PlotRange->2.5,AspectRatio->Automatic,PlotStyle->{PointSize[0.02],Blue},Epilog->{PointSize[0.05],Point[{0,0}]},PlotLabel->"Planetary Motion"],{theta,0,2Pi}]