{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 "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 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 119 "phug := [ diff(thet a(t),t) = (v(t)^2 - cos(theta(t)))/v(t),\n diff(v(t),t) \+ = -sin(theta(t)) - R*v(t)^2 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% phugG7$/-%%diffG6$-%&thetaG6#%\"tGF-*&,&*$)-%\"vGF,\"\"#\"\"\"F5-%$cos G6#F*!\"\"F5F2F9/-F(6$F2F-,&-%$sinGF8F9*&%\"RGF5F1F5F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 5 "R:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" RG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "DEplot(phug, [t heta,v], t=0..5, [[theta(0)=0, v(0)=1.5], [theta(0)=-Pi, v(0)=1] ], th eta=-Pi..Pi, v=0.1..3,\nlinecolor=black);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6]dl7%7$$!3\"QZ*yN'RpI$ !#<$\"3%\\:n+++++\"!#=7$$!3QE0@scCwHF*$\"2;XG$**********F-7$$!3ds7a:I% y/$F*$\"3oMhkt%*y!>\"F-7%7$$!3)e2YCi*zvHF*$\"3WwS2Dr\")R%*!#>7$$!3YHgR ex*fk#F*$\"3Y#f#\\(G=g0\"F-7$$!3$otQ*3iV?FF*$\"3KnRAYk.A7F-7%7$$!3+$Q' z\\dIVEF*$\"32x1xx\">ku)F>7$$!3\\Fy)Qq.rJ#F*$\"3SKHA#3e`7\"F-7$$!3=(Q0 !)e=XR#F*$\"36NK+iVFf7F-7%7$$!3=Kz[U.t1BF*$\"3l#yTh`#yOwF>7$$!3C$QQS= \"H#*>F*$\"3%=#eQYF*$\"3Mq$yV07O:&F>7$$!3'zIJ5 [Ex\"F*$\"3=SqWLV;A9F-7%7$$!3#H`u,9SaV\"F*$\"3::[bYr:mFF>7$$!3-$*f.Kb! 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