Hyperbolic Cylinder

d\[Theta] =
  Interpolation[{{0, 0}, {1, 2 Pi/3}, {2, 2 Pi/3}, {3, 0}},
   InterpolationOrder -> 1];
z0 = Interpolation[{{0, 900}, {1, 900}, {2, -900}, {3, -900}},
   InterpolationOrder -> 1];
x0 = Interpolation[{{0, 0}, {1, 0}, {1.5, 20}, {2, 0}, {3, 0}},
   InterpolationOrder -> 1];
x[t_] := 900 Exp[-10 (t - 1.5)^2];
z[t_] := -900 Tanh[5 (t - 1.5)];
frame[t_] := Module[{p0, p1},
   p0 = {Sin[d\[Theta][t]], Cos[d\[Theta][t]], 1};
   p1 = {0, 1, 0};
   Graphics3D[
    {White, Thickness[0.005],
     Table[
      Line[{RotationTransform[\[Theta], {0, 0, 1}][p0],
        RotationTransform[\[Theta], {0, 0, 1}][p1]}],
      {\[Theta], 0, 2 Pi, 2 Pi/20}]
     , FaceForm[], EdgeForm[Directive[Thickness[0.005], White]],
     Cylinder[{{0, 0, 0}, {0, 0, 1}}, 1]}
    , Boxed -> False, ViewPoint -> {x[t], 0, z[t]},
    ImageSize -> {300, 300}, Background -> Black]
   ];
Manipulate[
 frame[t],
 {t, 0, 3}]