{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 0 0 0 0 0 0 1 }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 0 1 } 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Outpu t" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 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 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 255 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "c International Thomson Pu blishing Bonn 1995 filename: numnewt.ms" }} {PARA 0 "" 0 "" {TEXT -1 102 "Autor: Komma \+ Datum: 8.5.94" }} {PARA 0 "" 0 "" {TEXT -1 61 "Thema: Prozedur zur numerischen L\366sung der Bewegungsgleichung" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 61 "restart;with(linalg,vector):with(student,equ ate):with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name ch angecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "hnumnewt:=TEXT(`FUNKTION: Berechnung einer numerischen L\366su ng der Bewegungsgleichung.`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "`AU FRUF: numnewton(Kraftgesetzt, Anfangsbedingungen).`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "`PARAMETER:`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "`Kraftgesetz: Vektor der Kraftkomponenten als Funktion (von x, v, \+ ...)`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "`Anfangsbedingungen: die \+ Menge der sechs Anfangswerte von Ort und Geschwindigkeit. `," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "`ERGEBNIS:`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "`Numnewton stellt die L\366sungen`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "`solp mit output=procedurelist und`," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "`soll mit output=listprocedure \+ zur Verf\374gung.`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "`Au\337erde m erh\344lt man die Vektoren rfn und vfn als Funktionen der Zeit, sowi e die table afn.`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "`Alle genannt en Variablen sind global.`," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "`Auf die Loesungen solp und soll kann mit odeplot([xn(t)...]) zugegriffen \+ werden`, " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "`wenn diese Namen nich t schon belegt sind ...` );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)hnum newtG-%%TEXTG6/%`oFUNKTION:~Berechnung~einer~numerischen~L|azsung~der~ Bewegungsgleichung.G%UAUFRUF:~numnewton(Kraftgesetzt,~Anfangsbedingung en).G%+PARAMETER:G%`oKraftgesetz:~Vektor~der~Kraftkomponenten~als~Funk tion~(von~x,~v,~...)G%]pAnfangsbedingungen:~die~Menge~der~sechs~Anfang swerte~von~Ort~und~Geschwindigkeit.~G%*ERGEBNIS:G%>Numnewton~stellt~di e~L|azsungenG%Gsolp~mit~output=procedurelist~~~~~~undG%Rsoll~mit~outpu t=listprocedure~~~~~~zur~Verf|gzgung.G%epAu|jxerdem~erh|_ylt~man~die~V ektoren~rfn~und~vfn~als~Funktionen~der~Zeit,~sowie~die~table~afn.G%FAl le~genannten~Variablen~sind~global.G%joAuf~die~Loesungen~solp~und~soll ~kann~mit~odeplot([xn(t)...])~zugegriffen~werdenG%Mwenn~diese~Namen~ni cht~schon~belegt~sind~...G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "#hnumnewt;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "** ** Zur Unterscheidung von der geschlossenen L\366sung enden die Variab lennamen auf \"n\" ****" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "numnewton:=proc(F,ini) global rn,vn ,an,xn,yn,zn,rfn,vfn,afn,soll,solp,sys;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "with(linalg,vector):with(student,equate):with(plots):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "unassign('xn(t)','yn(t)','zn(t)','x 0','vx0','y0','vy0','z0','vz0');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "rn:=vector([xn(t),yn(t),zn(t)]) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "vn:=map(diff,rn,t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "an:=map(diff,vn,t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sys:=equate(m*a n,F);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "solp:=dsolve(sys union ini ,\{xn(t),yn(t),zn(t)\},numeric,output=procedurelist);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "soll:=dsolve(sys union ini,\{xn(t),yn(t),zn(t)\} ,numeric,output=listprocedure);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " #print(soll);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "rfn:=subs(soll,op(rn));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "vfn:=subs(soll,op(vn));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "#af:=subs(soll,evalm(op(F)/m));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "#af:=t->map(eval,subs(solp(t),evalm(F/m)));" }}{PARA 0 "" 0 "" {TEXT -1 550 "Mit den vorangehenden Zuweisungen f\374r af be kommt man Probleme: Es ist eine Frage der Priorit\344t (Nichtkommutati vit\344t) von () und []. Man kann so zwar af() numerisch berechnen, ab er nicht plotten (im Plot darf kein Argument angegeben werden). Auch l assen sich die folgenden drei Befehle nicht so ohne weiteres zusammenf assen (etwa mit for oder seq), aber so funktioniert wenigstens alles. \+ Das sind eben die Eigenarten der Maple-Sprache. \"Die Designer von Map le haben das so entschieden\" (Monagan). Also Sonderl\366sung, insbes. f\374r Phasenportraits mit af:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " afn[1]:=t->map(eval,subs(solp(t),(F[1]/m)));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "afn[2]:=t->map(eval,subs(solp(t),(F[2]/m)));" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "afn[3]:=t->map(eval,subs(solp(t),(F [3]/m)));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*numnewtonGR 6$%\"FG%$iniG6\"F)F)C1-%%withG6$%'linalgG%'vectorG-F,6$%(studentG%'equ ateG-F,6#%&plotsG-%)unassignG6+.-%#xnG6#%\"tG.-%#ynGF=.-%#znGF=.%#x0G. %$vx0G.%#y0G.%$vy0G.%#z0G.%$vz0G>%#rnG-F/6#7%F;F@FC>%#vnG-%$mapG6%%%di ffGFRF>>%#anG-FY6%FenFWF>>%$sysG-F36$*&%\"mG\"\"\"FgnF`o9$>%%solpG-%'d solveG6&-%&unionG6$F[o9%<%F;F@FC%(numericG/%'outputG%.procedurelistG>% %sollG-Feo6&FgoF[pF\\p/F^p%.listprocedureG>%$rfnG-%%subsG6$Fap-%#opG6# FR>%$vfnG-Fip6$Fap-F\\q6#FW>&%$afnG6#F`oRF=F)6$%)operatorG%&arrowGF)-F Y6$%%evalG-Fip6$-Fco6#Fao*&&T$FgqF`oF_o!\"\"F)F)6$F'Fao>&Ffq6#\"\"#RF= F)FiqF)-FY6$F^r-Fip6$Far*&&FerFjrF`oF_oFfrF)F)Fgr>&Ffq6#\"\"$RF=F)FiqF )-FY6$F^r-Fip6$Far*&&FerFesF`oF_oFfrF)F)FgrF)6.FRFWFgnF " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "Test der \+ Prozedur mit der Keplerbewegung:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "rb:='xn(t)'^2+'yn(t)^2'+'zn(t)'^2;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#rbG,(*$)-%#xnG6#%\"tG\"\"#\"\"\"F-*$)-%#ynGF*F,F-F -*$)-%#znGF*F,F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "F:=ve ctor([-'xn(t)'/rb^(3/2),-'yn(t)'/rb^(3/2),-'zn(t)'/rb^(3/2)]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7%,$*&-%#xnG6#%\"tG \"\"\"*$),(*$)F+\"\"#F/F/*$)-%#ynGF-F5F/F/*$)-%#znGF-F5F/F/#\"\"$F5F/! \"\"F@,$*&F8F/*$)F2#F?F5F/F@F@,$*&F " 0 "" {MPLTEXT 1 0 7 "m:=0.5:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 67 "numini:=\{xn(0)=1,D(xn)(0)=0,yn(0)=0,D(yn)(0)=1,zn( 0)=0,D(zn)(0)=1\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'numiniG<(/-%# xnG6#\"\"!\"\"\"/--%\"DG6#F(F)F*/-%#ynGF)F*/--F/6#F3F)F+/-%#znGF)F*/-- F/6#F:F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "numnewton(F,n umini);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"tG6\"6$%)operatorG%&a rrowGF&-%$mapG6$%%evalG-%%subsG6$-%%solpG6#9$*&&T$6#\"\"$\"\"\"%\"mG! \"\"F&F&6$%\"FGF>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "sys;" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#<%/,$-%%diffG6$-%#znG6#%\"tG-%\"$G6$F ,\"\"#$\"\"&!\"\",$*&F)\"\"\"*$),(*$)-%#xnGF+F0F6F6*$)-%#ynGF+F0F6F6*$ )F)F0F6F6#\"\"$F0F6F3F3/,$-F'6$F@F-F1,$*&F@F6*$)F9#FEF0F6F3F3/,$-F'6$F " 0 "" {MPLTEXT 1 0 10 "rfn[1](8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3z`/_oh(z7$!#= " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "solp(8);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7)/%\"tG\"\")/-%#ynG6#F%$!3d#obodPir'!#=/-%%diffG6 $F(F%$\"3j/Zm2z(z7$F-/-%#znGF*F+/-F06$F5F%F2/-%#xnGF*$\"3z`/_oh(z7$F-/ -F06$F;F%$\"3jb[/T#[KM\"!#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "read `fig.m`:winpl():" }} {PARA 0 "" 0 "" {TEXT -1 46 "vtitle:=`x(t), v(t), a(t)`:vxlab:=t:vylab :=``:" }}{PARA 0 "" 0 "" {TEXT -1 83 "2d-Darstellung von Ort, Geschwin digkeit und Beschleunigung (jeweils in x-Richtung)." }}{PARA 0 "" 0 " " {TEXT -1 18 "pspl(`p1numn.ps`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(\{rfn[1],vfn[1],afn[1]\},0..4);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "R\344umliche Darstellung der Bahn. " }}{PARA 0 "" 0 "" {TEXT -1 97 "pspl(`p2numn.ps`):vtitle:=`Kepler-Ell ipse`:vxlab:=x:vylab:=y:vzlab:=z:xtick:=0:ytick:=0:ztick:=0:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plots[odeplot](solp,[xn(t),y n(t),zn(t)],0..5,axes=normal);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "Mathematisches Pendel" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "F:=vector([-sin(xn(t)),2,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"FG-%'vectorG6#7%,$-%$sinG6#-%#xnG6#%\"tG!\"\"\"\"#\"\"$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "numini:=\{xn(0)=1,D(xn)(0)=0 ,yn(0)=0,D(yn)(0)=1,zn(0)=0,D(zn)(0)=1\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'numiniG<(/-%#xnG6#\"\"!\"\"\"/--%\"DG6#F(F)F*/-%#ynG F)F*/--F/6#F3F)F+/-%#znGF)F*/--F/6#F:F)F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "numne wton(F,numini);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"tG6\"6$%)oper atorG%&arrowGF&-%$mapG6$%%evalG-%%subsG6$-%%solpG6#9$*&&T$6#\"\"$\"\" \"%\"mG!\"\"F&F&6$%\"FGF>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "pspl (`p3numn.ps`):vtitle:=`x(t), v(t), a(t)`:vxlab:=t: vylab:=``:xtick:=2: ytick:=2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot(\{rfn[1], vfn[1],afn[1]\},0..4);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Raumkurve" }}{PARA 0 "" 0 "" {TEXT -1 63 "pspl(`p4numn.ps`):vtit le:=Raumkurve:xtick:=0:ytick:=0:ztick:=0:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 51 "odeplot(solp,[xn(t),yn(t),zn(t)],0..8,axes=normal); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 175 "Mit odeplot \+ nimmt man \374ber interne Substitution Bezug auf die in der DG vorkomm enden Funktionen. Leider ist immer noch der horizontale Bereich mit de m Zeitparameter gekoppelt." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "Phasenportraits" }}{PARA 0 "" 0 "" {TEXT -1 62 "p spl(`p5numn.ps`):vtitle:=`y(x)`:xtick:=2:ytick:=2:vxlab:=`x`:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "odeplot(soll,[xn(t),yn(t)],- 2..2);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "odeplot (solp,[yn(t),xn(t)],-2..2);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 42 "#pspl(`p6numn.ps`):vtitle:=Phasenportrait:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "odeplot(solp,[xn(t),diff(xn( t),t)],-3..3);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "solp(4) ;" }}{PARA 0 "" 0 "" {TEXT -1 5 "soll;" }}{PARA 0 "" 0 "" {TEXT -1 8 " soll(4);" }}{PARA 0 "" 0 "" {TEXT -1 11 "***********" }}{PARA 0 "" 0 " " {TEXT -1 97 "Alternative Art des Zugriffs auf die L\366sungsgesamthe it mit normalen Plot-Befehlen (ohne " 0 "" {MPLTEXT 1 0 65 "plot(\{rhs(soll[1]),rhs(soll[2]),rh s(soll[3]),rhs(soll[4])\},0..3);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Phasenportraits (incl. Bahn aber o hne Beschleunigung s.u.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot([rhs(soll[1]),rhs(soll[4]),0..3]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 16 "So geht es auch:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "spacecurve([rhs(soll[2]),rhs(soll[4]),rhs(soll[6])],0 ..3,color=red);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 316 "Sonderfall des v-a-Phasenportraits: um \+ \"cannot evaluate boolean\" zu vermeiden, mu\337 die Auswertung der zu zeichnenden Funktion durch ' ' unterdr\374ckt werden, bis von dem plo t-Befehl f\374r t eine Zahl eingesetzt wird. Diese Art des parametrisc hen Plots kann nat\374rlich auch f\374r alle anderen Phasenportraits b en\374tzt werden." }}{PARA 0 "" 0 "" {TEXT -1 62 "pspl(`p8numn.ps`):vt itle:=`a-v-Portrait`:vxlab:=v:vylab:=`a `:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 39 "plot(['vfn[1](t)','afn[1](t)',t=0..8]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "== ==================================" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 47 "Ab hier nur noch Tests zu af(t)[i] ... un d plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "af:=t->map(eval,s ubs(solp(t),(F[1]/m))); # also mit einer Komponente des Vektors " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afGR6#%\"tG6\"6$%)operatorG%&arrowG F(-%$mapG6$%%evalG-%%subsG6$-%%solpG6#9$*&&%\"FG6#\"\"\"F;%\"mG!\"\"F( F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(convert(af,set ),0..6); # funktioniert" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "af(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+KwC2@!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "af:=t ->map(eval,subs(solp(t),evalm(F/m))); # ganzer Vektor" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afGR6#%\"tG6\"6$%)operatorG%&arrowGF(-%$mapG6$% %evalG-%%subsG6$-%%solpG6#9$-%&evalmG6#*&%\"FG\"\"\"%\"mG!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(af[1],0..6);" }} {PARA 8 "" 1 "" {TEXT -1 26 "Plotting error, empty plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "af:=F/m;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afG,$%\"FG$\"+++++?!\"*" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 15 "af:=evalm(F/m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#afG-%'vectorG6#7%,$-%$sinG6#-%#xnG6#%\"tG$!+++++?!\"*$\"+++++SF3$\" +++++gF3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "af:=subs(solp(t ),evalm(F/m));" }}{PARA 8 "" 1 "" {TEXT -1 64 "Error, (in solp) cannot evaluate boolean: abs(t)-abs(-6.+t) < 0\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 29 "af:=subs(solp(6),evalm(F/m));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afG-%'vectorG6#7%,$-%$sinG6#$!3;u\"\\9/$eb5!#=$!++++ +?!\"*$\"+++++SF2$\"+++++gF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "af:=eval(subs(solp(6),evalm(F/m)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afG-%'vectorG6#7%,$-%$sinG6#$!3;u\"\\9/$eb5!#=$!++++ +?!\"*$\"+++++SF2$\"+++++gF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "af:=map(eval,subs(solp(6),evalm(F/m)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afG-%'vectorG6#7%$\"+MwC2@!#5$\"+++++S!\"*$\"+++++gF ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "af:=t->map(eval,subs(s olp(t),evalm(F/m)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#afGR6#%\"tG 6\"6$%)operatorG%&arrowGF(-%$mapG6$%%evalG-%%subsG6$-%%solpG6#9$-%&eva lmG6#*&%\"FG\"\"\"%\"mG!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "af(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6# 7%$\"+MwC2@!#5$\"+++++S!\"*$\"+++++gF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "af(6)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+MwC2@ !#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Plot: vgl. Monagan, Tips f or Maple Users in MapleTech Issue 10 Fall 1993, p11" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot(af,0..6);" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plotting error, empty plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(af[1],0..6);" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plo tting error, empty plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " af;op(af);eval(af);evalm(af);whattype(af);whattype(af(6));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#afG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6# %\"tG6\"6$%)operatorG%&arrowGF&-%$mapG6$%%evalG-%%subsG6$-%%solpG6#9$- %&evalmG6#*&%\"FG\"\"\"%\"mG!\"\"F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"tG6\"6$%)operatorG%&arrowGF&-%$mapG6$%%evalG-%%subsG6$-%%s olpG6#9$-%&evalmG6#*&%\"FG\"\"\"%\"mG!\"\"F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#afG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'symbolG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "whattype(af());" }}{PARA 8 "" 1 "" {TEXT -1 59 "Error , (in af) af uses a 1st argument, t, which is missing\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "whattype(af(t));" }}{PARA 8 "" 1 " " {TEXT -1 64 "Error, (in solp) cannot evaluate boolean: abs(t)-abs(-6 .+t) < 0\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "whattype(af(6 ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "af(6)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+MwC2@!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "af[1](6);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+MwC2@!#5$\"+++++S!\" *$\"+++++gF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "af[1](7);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+!)Ges;!\"*$\"+++++S F)$\"+++++gF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "af[100](7) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+!)Ges;!\"*$\"++ +++SF)$\"+++++gF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "af[uiu iuiuiu](7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+!)Ges ;!\"*$\"+++++SF)$\"+++++gF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "af[](7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+!)Ges ;!\"*$\"+++++SF)$\"+++++gF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "af(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%$\"+!)Ges;! \"*$\"+++++SF)$\"+++++gF)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "() h at Priorit\344t: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ax:=t- >af(t)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#axGR6#%\"tG6\"6$%)ope ratorG%&arrowGF(&-%#afG6#9$6#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 6 "ax(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+%[Zs5# !#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(ax,0..5); # fun ktioniert" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 43 "plot(t->af(t)[1],0..5); # funktioniert auch" }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Also liegt es am assignm ent." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "komma@oe.uni-tuebingen.de" }}}}{MARK "0 0 0" 8 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }