{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{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" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 227 "R:=`R`:\nxphug :=[ \+ diff(theta(t),t) = (v(t)^2 - cos(theta(t)))/v(t),\n diff(v(t ),t) = -sin(theta(t)) - R*v(t)^2 ,\n diff(x(t),t) = \+ v(t)*cos(theta(t)),\n diff(y(t),t) = v(t)*sin(theta(t)) ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&xphugG7&/-%%diffG6$-%&thetaG6 #%\"tGF-*&,&*$)-%\"vGF,\"\"#\"\"\"F5-%$cosG6#F*!\"\"F5F2F9/-F(6$F2F-,& -%$sinGF8F9*&%\"RGF5F1F5F9/-F(6$-%\"xGF,F-*&F2F5F6F5/-F(6$-%\"yGF,F-*& F2F5F>F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "phug := [ xphug [1], xphug[2] ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%phugG7$/-%%diff G6$-%&thetaG6#%\"tGF-*&,&*$)-%\"vGF,\"\"#\"\"\"F5-%$cosG6#F*!\"\"F5F2F 9/-F(6$F2F-,&-%$sinGF8F9*&%\"RGF5F1F5F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "phugR:= subs( \{v(t)=v, theta(t)= theta\}, \n \+ map( rhs, phug));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&phugRG7$ *&,&*$)%\"vG\"\"#\"\"\"F,-%$cosG6#%&thetaG!\"\"F,F*F1,&-%$sinGF/F1*&% \"RGF,F)F,F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg ):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm a nd trace have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "J:=jacobian(phugR, [theta,v]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"JG-%'matrixG6#7$7$*&-%$sinG6#%&thetaG\"\"\"%\" vG!\"\",&\"\"#F/*&,&*$)F0F3F/F/-%$cosGF-F1F/F0!\"#F17$,$F8F1,$*&%\"RGF /F0F/F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Jac0:=evalf(subs (\{R=0,v=1,theta=0.0\}, evalm(J))); " }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%%Jac0G-%'matrixG6#7$7$$\"\"!F+$\"\"#F+7$$!\"\"F+F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eigenvals(Jac0);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$^$$\"\"!F%$\"+iN@99!\"*^$F$$!+iN@99F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "trace(Jac0); det(Jac0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"!F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"\"#\"\"!" }}}}{MARK "8" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }