Using RotationTransform and Table

Question

I created a small animation, very simple of course, that works very well.

Export["C:\\Users\\LMC\\Desktop\\Figure.gif",Flatten@@Table[Graphics[{Point[{0,0}],GeometricTransformation[Circle[{0,-20},2],RotationTransform[(50Sin[#-(3 π)/2]) Degree]]},PlotRange->{{20,-20},{-25,25}},Axes->True],1]&/@Range[0,10,0.05]]

In the future I will create animations that I intend to subdivide using $r1$, $r2$, $r3$, $r4$ and $r5$. All with different characteristics, but all varying equally with Range [0,10,0.05].

I tried to do a test with a value $r1$ based on the successful animation above, but at the beginning, two problems arose.

Surely this must be something very simple and possibly this question can be a duplicate.

The first problem was that the starting position is not the same as that of the previous animation. I tried to make $r1$ as an "argument" for substitution.

The second problem was that all frames were the same.

r1=GeometricTransformation[Circle[{0,-20},2],RotationTransform[(50Sin[#-(3 π)/2]) Degree]];
Export["C:\\Users\\Leandro\\Desktop\\Figure.gif",Flatten@@Table[Graphics[{Point[{0,0}],r1},PlotRange->{{20,-20},{-25,25}},Axes->True],1]&/@Range[0,10,0.05]]

I do not understand what might be wrong.

Answer 1

I think this might be what you are after:

r1 = RotationTransform[(50 Sin[# - (3 Pi)/2]) Degree]&;

frames = Graphics[
     {Point[{0, 0}],
      GeometricTransformation[
        Circle[{0, -20}, 2],
        r1[#]
      ]
     },
     PlotRange -> {{20, -20}, {-25, 25}}, Axes -> True
   ]& /@ Range[0, 10, 0.05];

You can take a look at the result within Mathematica using ListAnimate:

ListAnimate[frames]