{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 
1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 
0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 
"" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 
}{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 
2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):
" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has be
en redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "x:=t->t;y
:=t->sin(t/2+cos(t)/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGj+6#%
\"tG6\"6$%)operatorG%&arrowGF(9$F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"yGj+6#%\"tG6\"6$%)operatorG%&arrowGF(-%$sinG6#,&*&#
\"\"\"\"\"#F29$F2F2*&F1F2-%$cosG6#F4F2F2F(F(F(6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot([x(t),y(t),t=0..16],x=-1..16,y
=-5..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dx:=D(x);dy:=D(
y);r:=t->sqrt(dx(t)^2+dy(t)^2);r(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#dxG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dyGj+6#%\"tG6\"6$
%)operatorG%&arrowGF(*&-%$cosG6#,&*&#\"\"\"\"\"#F39$F3F3*&F2F3-F.6#F5F
3F3F3,&F2F3*&#F3F4F3-%$sinGF8F3!\"\"F3F(F(F(6#\"\"!" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"rGj+6#%\"tG6\"6$%)operatorG%&arrowGF(-%%sqrtG6#,&
*$)-%#dxG6#9$\"\"#\"\"\"F7*$)-%#dyGF4F6F7F7F(F(F(6#\"\"!" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*$,&\"\"\"F%*&)-%$cosG6#,&*&\"\"#!\"\"%\"tGF%F%*
&#F%F-F%-F)6#F/F%F%F-F%),&F1F%*&#F%F-F%-%$sinGF3F%F.F-F%F%F1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "x2:=t->x(t)+dx(t)/r(t);x2(t)
;y2:=t->y(t)+dy(t)/r(t);y2(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x
2Gj+6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%\"xG6#9$\"\"\"*&-%#dxGF/F1-%
\"rGF/!\"\"F1F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"tG
\"\"\"*&F%F%*$,&F%F%*&)-%$cosG6#,&*&\"\"#!\"\"F$F%F%*&#F%F0F%-F,6#F$F%
F%F0F%),&F3F%*&#F%F0F%-%$sinGF5F%F1F0F%F%#F%F0F1F%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#y2Gj+6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%\"yG6#9$
\"\"\"*&-%#dyGF/F1-%\"rGF/!\"\"F1F(F(F(6#\"\"!" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&-%$sinG6#,&*&\"\"#!\"\"%\"tG\"\"\"F,*&#F,F)F,-%$cosG6
#F+F,F,F,*(-F0F&F,,&F.F,*&#F,F)F,-F%F1F,F*F,,&F,F,*&)F3F)F,)F4F)F,F,#F
*F)F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "plot([[x(t),y(t),
t=0..16],[x2(t),y2(t),t=-0.75..16]],x=-1..16,y=-5..5, scaling=constrai
ned,color=[blue,red],axes=none,thickness=[1,1]);P:=%:" }}}{EXCHG }
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 246 "animate( plot, [[[x(r)+0.05
*cos(t),y(r)+0.05*sin(t),t=0..2*Pi], [x2(r)+0.05*cos(t),y2(r)+0.05*sin
(t),t=0..2*Pi], [t*x2(r)+x(r)*(1-t),t*y2(r)+y(r)*(1-t),t=0..1]], color
=[black,black,black]], r=0..16, scaling=constrained, frames=101,backgr
ound=P );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 \+
0 0" 20 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }