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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 11 "Feb 24 2004" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "phug:=[diff(thet
a(t),t)=(v(t)^2-cos(theta(t)))/v(t), diff(v(t),t)=-sin(theta(t))-R*v(t
)^2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phugG7$/-%%diffG6$-%&theta
G6#%\"tGF-*&,&*$)-%\"vGF,\"\"#\"\"\"F5-%$cosG6#F*!\"\"F5F2F9/-F(6$F2F-
,&-%$sinGF8F9*&%\"RGF5F1F5F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 81 "fixept:=convert(solve(\{(v^2-cos(theta))/v,-sin(theta)-R*v^2\},
\{theta,v\}),radical);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'fixeptG<$
/%\"vG*$)*&\"\"\"F+,&*$)%\"RG\"\"#F+F+F+F+!\"\"#F+\"\"%F+/%&thetaG-%'a
rctanG6$,$*&F/F+F*#F+F0F1*$F*F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 79 "with(linalg):\nJ:=jacobian([(v^2-cos(theta))/v,-sin(theta)-R*v
^2],[theta,v]);\n\n\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the pro
tected names norm and trace have been redefined and unprotected\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'matrixG6#7$7$*&-%$sinG6#%&the
taG\"\"\"%\"vG!\"\",&\"\"#F/*&,&*$)F0F3F/F/-%$cosGF-F1F/F0!\"#F17$,$F8
F1,$*(F3F/%\"RGF/F0F/F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "
trfix:=   simplify(subs(fixept,trace(J)));\ndetfix:=  simplify(subs(fi
xept,det(J)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&trfixG,$*(\"\"$\"
\"\"%\"RGF()*&F(F(,&*$)F)\"\"#F(F(F(F(!\"\"#F(\"\"%F(F0" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%'detfixG,$*&\"\"#\"\"\"*&F(F(,&*$)%\"RGF'F(F(F
(F(!\"\"#F.F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEt
ools):" }}{PARA 7 "" 1 "" {TEXT -1 45 "Warning, the name adjoint has b
een redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "R:=1;\n
DEplot(phug,[theta(t),v(t)],t=-2..5,[seq([theta(0)=0,v(0)=1+0.2*i],i=0
..10)],\ntheta=-2..2,v=0.01..3,linecolor=black,stepsize=0.1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG\"\"\"" }}{PARA 13 "" 1 "" 
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