How can I animate a point on a polar curve? I have used Animate
and Show
together before in order to get the curve and the moving point together on the same plot, but combining the polar plot and the point doesn't seem to be working because point only works with Cartesian coordinates.
Here is the code I used before to animate a point on a parametric curve. For higher values of a
and theta
, you can see the point moving along the curve better (I was required to animate all three parameters).
Animate[
Show[
ParametricPlot[{a Cos[θ] t, a Sin[θ] t - 4.9 t^2}, {t, 0, 15}, AxesLabel -> {"x", "y"},
PlotRange -> {{0, 50}, {0, 30}}],
Graphics[{Red, PointSize[.05], Point[{a Cos[θ] t, a Sin[θ] t - 4.9 t^2}]}]
],
{t, 0, 5, Appearance -> "Labeled"},
{a, 1, 20, Appearance -> "Labeled"},
{θ, 0, Pi/2, Appearance -> "Labeled"},
AnimationRunning -> False
]
Here is the code I tried to use to animate a point on a polar curve, but the point does not even show up.
Animate[
Show[
PolarPlot[2 Sin[4*θ], {θ, 0, 2 Pi}],
Graphics[Red, PointSize[Large], Point[{2 Sin[4*θ] Cos[θ], 2 Sin[4*θ] Sin[θ]}]]
],
{θ, 0, 2 Pi},
AnimationRunning -> False
]