{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 10 255 0 0 1 2 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 "Helvetica" 1 10 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE " " -1 -1 "Helvetica" 1 10 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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Helvetica " 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 6 6 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "New Page" -1 256 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 1 2 0 1 }{PSTYLE "SubTitle" -1 257 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 4 4 1 0 1 0 2 2 0 1 }{PSTYLE "Date" -1 258 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 } 3 1 0 0 2 2 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 15 "Swimmer Problem" }}{PARA 257 "" 0 "" {TEXT -1 9 " MA 238-01" }}{PARA 258 "" 0 "" {TEXT -1 13 "June 22, 2001" }}{PARA 19 "" 0 "" {TEXT -1 12 "Richard Hitt" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "Introduction" }}{PARA 0 "" 0 "" {TEXT -1 93 "This worksheet dis cusses the swimmer problem in section 1.9 of the Borrelli and Coleman \+ book." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 15 "Getting started" }} {PARA 0 "" 0 "" {TEXT -1 140 "Every Maple worksheet should begin by re -initializing the Maple \"kernel\" and loading the additional packages that we are most likely to use." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "Example" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Fi rst we set some of the values to look at a specific example." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=1; s:=1;c:=.5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG$\"\"&!\" \"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Then we solve the different ial equation." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "dsolve(\{d iff(y(x),x)=(y(x)-(c/s)*sqrt(x^2+y(x)^2))/x,y(a)=0\},y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG-%'RootOfG6#,(%#_ZG\"\"\"*$-%% sqrtG6#,&*$)F'\"\"#F-F-*$)F,F5F-F-F-F-*$-F06#F'F-!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Then plot the curve." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "plot(rhs(%),x=0..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7gn7$$\"\"!F)F(7$$\"+ N@Ki8!#7$\"+r#oH%=!#67$$\"+qUkCFF-$\"+#>&z-EF07$$\"+0k'p3%F-$\"+TaS$=$ F07$$\"+S&)G\\aF-$\"+%p^3n$F07$$\"+5G$R<)F-$\"+e+a$[%F07$$\"+3x&)*3\"F 0$\"+')R#H;&F07$$\"+ilyM;F0$\"+4xU)G'F07$$\"+;arz@F0$\"+'fC5A(F07$$\"+ !y%*z7$F0$\"+t#ekc)F07$$\"+XTFwSF0$\"+fpR$o*F07$$\"+oMrU^F0$\"+0bcv5!# 57$$\"+\"z_\"4iF0$\"+:#[&o6F]o7$$\"+m6m#G(F0$\"+\")Q0^7F]o7$$\"+S&phN) F0$\"+IfdC8F]o7$$\"+*=)H\\5F]o$\"+8Zp\\9F]o7$$\"+[!3uC\"F]o$\"+&G\\ca \"F]o7$$\"+J$RDX\"F]o$\"+'R7)G;F]o7$$\"+)R'ok;F]o$\"+swU+F]o7$$\"+(*ev:JF]o$\"+3mN@>F]o7$$\"+347TLF]o$\"+ip\\C>F]o7 $$\"+LY.KNF]o$\"+ld)>#>F]o7$$\"+\"o7Tv$F]o$\"+5IX8>F]o7$$\"+$Q*o]RF]o$ \"+jA8,>F]o7$$\"+\"=lj;%F]o$\"+D%HF)=F]o7$$\"+V&RY2aF]o$\"+(pr&)o\"F]o 7$$\"+yXu9cF]o$\"+65(Hk\"F]o7$$\"+\\y))GeF]o$\"+)piAf\"F]o7$$\"+i_QQgF ]o$\"+FpAR:F]o7$$\"+!y%3TiF]o$\"+(f\"y%[\"F]o7$$\"+O![hY'F]o$\"+Dp#3U \"F]o7$$\"+#Qx$omF]o$\"+PPIg8F]o7$$\"+u.I%)oF]o$\"+FUd#H\"F]o7$$\"+(pe *zqF]o$\"+Px\\G7F]o7$$\"+C\\'QH(F]o$\"+?bdb6F]o7$$\"+8S8&\\(F]o$\"+woG %3\"F]o7$$\"+0#=bq(F]o$\"+j/125F]o7$$\"+2s?6zF]o$\"+I.Q*G*F07$$\"+IXaE \")F]o$\"+-ANW%)F07$$\"+l*RRL)F]o$\"+[cw/wF07$$\"+`<.Y&)F]o$\"+Ole?nF0 7$$\"+8tOc()F]o$\"+P_n=eF07$$\"+\\Qk\\*)F]o$\"+.*=$o\\F07$$\"+p0;r\"*F ]o$\"+l\"R(oRF07$$\"+lxGp$*F]o$\"+4@\\_IF07$$\"+!oK0e*F]o$\"+hr(G0#F07 $$\"+<5s#y*F]o$\"+dv_u5F07$$\"\"\"F)F(-%'COLOURG6&%$RGBG$\"#5!\"\"F(F( -%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F(Fe]l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 223 " This time we start again and leave the parameters unspecified so we ca n plot a collection of curves. 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