Two animations on the same ListAnimate plot

Question

I have a code that produces two lists to be animated using ListAnimate and I want to have these two animations taking place on the same plot but I can't see a clear way to do this and was wondering if anyone could help or had any ideas?

The values I am using are:

cVal = {1., 0.8090169943749475, 
   0.30901699437494745, -0.30901699437494745, -0.8090169943749475, 
-1., -0.8090169943749475, -0.30901699437494745, 
   0.30901699437494745, 0.8090169943749475, 1.};


sVal = {0., 0.5877852522924731, 0.9510565162951535, 
   0.9510565162951535, 0.5877852522924731, 
   0., -0.5877852522924731, -0.9510565162951535, 
-0.9510565162951535, -0.5877852522924731, 0.};


solVals = {{0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 
    0.125, 0.125, 0.125, 0.125}, {0.12490148827035571, 
    0.12464449866763125, 0.12442505176003116, 0.1244223463177388, 
    0.12463736991663273, 0.12499191997994591, 0.1253531547434718, 
    0.12558070842365024, 0.12558354323701965, 0.12536051828017497, 
    0.1250994004033477}, {0.12480384709546988, 0.1242939341780157, 
    0.12385862558252374, 0.12384799275047834, 0.12426573496222888, 
    0.12496769300729224, 0.12569636813682097, 0.12616421257572788, 
    0.12617574946914567, 0.1257261340087955, 
    0.1251997082335011}, {0.12470708257569338, 0.12394825285367117,
     0.12330064002945827, 0.12327715902511607, 0.12388555678367119,
     0.1249273562850483, 0.12602919036770016, 0.1267502550644418, 
    0.1267766885931119, 0.12609690114465189, 
    0.12530091727743586}, {0.12461120068883887, 0.1236073951160553,
     0.12275100275202656, 0.12271007702920879, 0.12349734772541728,
     0.1248709740470937, 0.12635112913506485, 0.1273385398615683, 
    0.12738643468770763, 0.12647287907280338, 
    0.12540301988421534}, {0.12451620597345099, 
    0.12327130632752725, 0.12220962673019696, 0.12214694486285972, 
    0.12310157717049357, 0.1247986333640127, 0.12666174196262933, 
    0.1279287826296457, 0.1280050512784557, 0.1268541216286478, 
    0.12550600807208026}, {0.12442210234560008, 
    0.12293993046137541, 0.12167642116190003, 0.12158795438046, 
    0.12269872499996635, 0.12471044547575386, 0.12696058324786766, 
    0.1285206818181489, 0.12863259986320424, 0.1272406834263168, 
    0.12560987281940664}, {0.12432889300763066, 
    0.12261321145350433, 0.12115129358146054, 0.12103328614526516, 
    0.12228926966459856, 0.12460654426849799, 0.1272472158550164, 
    0.12911392521428341, 0.12926913806764226, 0.12763261852451369, 
    0.12571460421758704}, {0.12423658035218303, 
    0.12229109323322443, 0.12063414972822373, 0.12048310761517643, 
    0.12187368710919808, 0.12448708981559341, 0.12752121342394807, 
    0.1297081883650303, 0.12991471880821223, 0.1280299802631563, 
    0.12582019128605407}, {0.12414516614006692, 
    0.12197351978111352, 0.12012489409055069, 0.11993757558871533, 
    0.12145245000629556, 0.12435226329714764, 0.12778215973303794, 
    0.13030313710125782, 0.13056939084851202, 0.12843282129358177, 
    0.12592662211972083}, {0.12405465147008787, 0.1216604351616048,
     0.11962342991308532, 0.11939683547817558, 0.12102602690488753,
     0.12420226834101644, 0.12802965013098178, 0.13089842700822404,
     0.13123319833473931, 0.12884119346758624, 
    0.12603388378961122}};

These give the following plots

base = Table[
   ListLinePlot[Partition[Riffle[Flatten[cVal], Flatten[sVal]], 2], 
    AspectRatio -> Full], {l, 1, 11}];

outer = Table[
   ListLinePlot[
    Partition[
     Riffle[Table[solVals[[j]]*cVal + cVal, {j, 1, 11}][[l]], 
      Table[solVals[[j]]*sVal + sVal, {j, 1, 11}][[l]]], 2], 
    AspectRatio -> Full, PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}], {l,1, 11}];

Using ListAnimate[base] gives a fixed plot centred at the origin and ListAnimate[outer] gives another plot initially fixed on the origin but moves away from its initial position as time passes.

Answer 1

First an alternative, more streamlined, way to construct outer:

tbl = Transpose[{cVal + cVal #, sVal + sVal #}] & /@ solVals; 

outer2 = ListLinePlot[#, 
  AspectRatio -> Full, 
  PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}] & /@ tbl;

outer2 == outer

True

baseplot = ListLinePlot[Transpose[{cVal, sVal}], PlotStyle -> Red];

ListAnimate[Show[#, baseplot] & /@ outer2]

The movement is almost imperceptible.

Using scaled-up versions of the input data makes the movement more visible:

tblB = Transpose[{cVal + cVal #, sVal + sVal #}] & /@ (10000 solVals); 

outer2B = ListLinePlot[#, AspectRatio -> Full, 
    PlotRange -> {1000 {-1.5, 1.5}, 1000 {-1.5, 1.5}}] & /@ tblB;

baseplotB = ListLinePlot[Transpose[1000 {cVal, sVal}], PlotStyle -> Red];

ListAnimate[Show[#, baseplotB] & /@ outer2B]