R:=`::R`: # R-radius of the large circle
r:=`::r`: # r-radius of the small circle
N:=`::N`: # N-number of frames of animation

A:=plot([R*cos(t),R*sin(t),t=0..2*Pi],color=blue,thickness=2):

B:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N),(R-r)*sin(2*Pi*k/N)],r,
color=yellow),k=1..N):

C:=seq(plottools[disk]([(R-r)*cos(2*Pi*k/N)+r*cos(2*Pi*k/N-R*2*Pi*k/r/N),
(R-r)*sin(2*Pi*k/N)+r*sin(2*Pi*k/N-R*2*Pi*k/r/N)],r/15,color=red),k=1..N):

F:=seq(plot([(R-r)*cos(t)+r*cos(t-R*t/r),(R-r)*sin(t)+r*sin(t-R*t/r),
t=0..2*Pi*k/N],x=-R..R,y=-R..R,color=red,thickness=2),k=1..N):

for k from 1 to N do E[k]:=plots[display](A,C[k],B[k],F[k]); od:

plots[display]([seq(E[k],k=1..N)],insequence=true,scaling=constrained,
view=[-R-1..R+1,-R-1..R+1]);

07.06.2013 23:02:12 [->] solve({(0=(77/10000*ln({((77/10000+772893421/100000000000000*t*715*cos({(Pi/4)}))/77/10000)}))/772893421/100000000000000)},t)
07.06.2013 23:02:12 [->] C:\Temp\tmp1B5E.tmp:
interface(quiet=true);
with(linalg):with(inttrans):with(plots):

writeto("C:\\Temp\\tmp1B5F.tmp"):
smath_line := proc() local i: for i from 1 to nargs - 2 do args[i]; od: end:
smath_sum := proc() if nargs = 1 then sum( args[1] ); elif nargs = 2 then sum( args[1], args[2] ); elif nargs = 4 then sum( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_product:= proc() if nargs = 1 then product( args[1] ); elif nargs = 2 then product( args[1], args[2] ); elif nargs = 4 then product( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_int := proc() if nargs = 2 then int( args[1], args[2] ); elif nargs = 4 then int( args[1], args[2] = args[3] .. args[4] ); fi: end:
smath_diff := proc() if nargs = 2 then diff( args[1], args[2] ); elif nargs = 3 then diff( args[1], args[2] $ args[3] ); fi: end:
smath_sys := proc() { args[i] $ i = 1 .. nargs - 2 }; end:
smath_el := proc() args[1][ args[2] ]; end:
smath_mat := proc()
local i, j, out:
out := [ args[j] $ j = 1 .. args[ nargs ] ]:
for i from 2 to args[ nargs - 1 ] do
out := out, [ args[j] $ j = ( i - 1 ) * args[ nargs ] + 1 .. ( i - 1 ) * args[ nargs ] + args[ nargs ] ]:
od:
convert( [ out ], array );
end:
smath_submatrix := proc() submatrix( args[1], args[2] .. args[3], args[4] .. args[5] ); end:
ans := \
solve(((0=(77/10000*ln((((77/10000+772893421/100000000000000*t*715*cos\
(((Pi/4))))/77/10000))))/772893421/100000000000000)),t):
if ( whattype( ans ) = `exprseq` ) then
convert( convert( cat( `mat(`, substring( convert( [ans], string ), 2..-2 ), `,`, nops( [ans] ), `,1)` ), string ), symbol );
elif ( whattype( ans ) = `set` ) then
convert( convert( cat(`mat(`,substring(convert(map2(op,2,[ans[i]$i=1..nops(ans)]),string),2..-2),`,`,nops(ans),`,1)`), string ), symbol );
elif ( whattype( ans ) = `symbol` ) then
convert( convert( eval( ans ), string ), symbol );
elif ( whattype( ans ) = `series` ) then
convert( convert( ans, polynom) , symbol );
elif ( whattype( ans ) = `string` ) then
convert( ans, symbol );
else
convert( convert( ans, string ), symbol ); fi;
quit:

07.06.2013 23:02:12 [<-] C:\Temp\tmp1B5F.tmp:
1399999986000000000/10047614473*2^(1/2)
07.06.2013 23:02:12 [<-] 1399999986000000000/10047614473*2^(1/2)