{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 "Maple Output" 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 "R 3 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: newtpro.ms" }} {PARA 0 "" 0 "" {TEXT -1 102 "Autor: Komma \+ Datum: 4.5.94" }} {PARA 0 "" 0 "" {TEXT -1 152 "Thema: Newtons Physik als procedure. Das Worksheet enth\344lt die procedure newton zur geschlossenen L\366sung der Bewegungsgleichung und Anwendungsbeispiele." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "Ben\366tigte packages" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "r estart;with(linalg):with(student):with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the \+ name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "Beginn der Prozedur" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "newton:=proc(F) global r,v,a,xx,yy,zz,rf,vf,af,sol,sys;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "#with(linalg):with(student):with(pl ots):readlib(unassign):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "#unassig n('x(t)','y(t)','z(t)');" }}{PARA 0 "" 0 "" {TEXT -1 447 "Es ist zweck m\344\337ig, auch die Anfangsbedingungen zur\374ckzusetzen, damit die \+ L\366sung jeweils in allgemeiner Form zur Verf\374gung steht, und konk rete Werte au\337erhalb der Prozedur und ohne neuen Aufruf eingesetzt \+ werden k\366nnen. Die \334bergabe der Anfangsbedingungen als Parameter der Prozedur w\344re m\366glich, w\374rde aber zuviel Schreibarbeit b eim Aufruf oder eine Abfrage der Argumente erfordern. Die Ortsfunktion en m\374ssen wegen sys (s.u.) zur\374ckgesetzt werden." }}{PARA 0 "" 0 "" {TEXT -1 228 "Ein konsequentes Umgehen der fr\374hen Bindung durc h einf\374hren weiterer Prozeduren w\374rde die \334bersichtlichkeit n icht erh\366hen. In diesem Stadium gen\374gt die Methode: \"mache aus \+ einem funktionierenden worksheet durch \"proc() ... end;\"" }}{PARA 0 "" 0 "" {TEXT -1 14 "eine Prozedur." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "unassign('x(t)','y(t)','z(t)','x0','vx0','y0','vy0','z0','vz0');" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "#x(0):='x0': D(x)(0):='vx0': y(0) :='y0': D(y)(0):='vy0':z(0):='z0': D(z)(0):='vz0';" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "r:=vector([x(t),y(t),z(t)]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "v:=map(diff,r,t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "a:=map(diff,v,t);" }}{PARA 0 "" 0 "" {TEXT -1 136 "Wenn sys in der proc steht und diese mehrfach aufgerufen wird, m\374ssen vorher die O rtsfunktionen mit unassign zur\374ckgesetz werden. (s.o.)" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "sys:=equate(m*a,F);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "#print(sys);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "sol:=dsolve(sys,\{x(t),y(t),z(t)\} ,method=laplace);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "print(sol);" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "if sol=NULL then sol:=dsolve(sys, \{x(t),y(t),z(t)\}) fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "if sol=N ULL then RETURN(`keine Loesung gefunden`) fi;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(sol);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "xx :=makeproc(x(t),t): yy:=makeproc(y(t),t): zz:=makeproc(z(t),t):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "rf:=makeproc(map(eval,r),t); vf:=ma keproc(map(eval,v),t); af:=makeproc(map(eval,a),t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "x(0):='x0': D(x)(0):='vx0': y(0):='y0': D(y)(0):=' vy0':z(0):='z0': D(z)(0):='vz0';" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "RETURN(op(rf));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'newtonGR6#%\"FG6\"F(F(C9-%)unassignG6+.-% \"xG6#%\"tG.-%\"yGF0.-%\"zGF0.%#x0G.%$vx0G.%#y0G.%$vy0G.%#z0G.%$vz0G>% \"rG-%'vectorG6#7%F.F3F6>%\"vG-%$mapG6%%%diffGFEF1>%\"aG-FM6%FOFKF1>%$ sysG-%'equateG6$*&%\"mG\"\"\"FQFen9$>%$solG-%'dsolveG6%FU<%F6F3F./%'me thodG%(laplaceG-%&printG6#Fhn@$/Fhn%%NULLG>Fhn-Fjn6$FUF\\o@$Fdo-%'RETU RNG6#%7keine~Loesung~gefundenG-%'assignGFbo>%#xxG-%)makeprocG6$F.F1>%# yyG-Fcp6$F3F1>%#zzG-Fcp6$F6F1>%#rfG-Fcp6$-FM6$%%evalGFEF1>%#vfG-Fcp6$- FM6$FcqFKF1>%#afG-Fcp6$-FM6$FcqFQF1>-F/6#\"\"!F8>--%\"DG6#F/FbrF:>-F4F brF<>--Fgr6#F4FbrF>>-F7FbrF@>--Fgr6#F7FbrFB-F[p6#-%#opG6#F^qF(6-FEFKFQ FapFfpFjpF^qFeqF[rFhnFUF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "#x(t):='x(t)':y(t):='y (t)':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "unassign('x(t)','y (t)','z(t)');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 463 "Wenn im Kraftge setz bereits zugewiesene Variable verwendet werden (z.B. x(t), v(t).. \+ ), ist es am einfachsten, diese nicht ausgewertet, also in '..' aufzuf \374hren. Alternative: kleine L\366schprozedur. Am Beispiel der ged \344mften Schwingung (in x-Richtung), der eine konstante Kraft \374ber lagert ist und einer gleichm\344\337ig beschleunigten Bewegung in y- u nd z-Richtung kann man die Formeln studieren, die von Maple geliefert \+ werden. Nat\374rlich kann man auch den Input \344ndern." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "unassign('Fx','Fy','Fz'):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "F:=vector([Fx-'x(t)+v[1]',Fy ,Fz]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7%,(%#FxG \"\"\"-%\"xG6#%\"tG!\"\"&%\"vG6#F+F0%#FyG%#FzG" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " newton(F);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%/-%\"xG6#%\"tG,8%#FxG \"\"\"*(#F+\"\"#F+-F&6#\"\"!F+-%$expG6#,$*&*&,&*$-%%sqrtG6#,&F+F+*&\" \"%F+%\"mGF+!\"\"F+F+F+F+F+F(F+F+F@FA#FAF.F+F+*(F-F+F/F+-F36#,$*&*&,&F 9F+F+FAF+F(F+F+F@FAF-F+F+*&#F+F.F+*&F*F+F2F+F+FA*&#F+F.F+*&F*F+FDF+F+F A*&*(F@F+--%\"DG6#F&F0F+F2F+F+*$-F;6#F=F+FAFA*&*(F@F+FRF+FDF+F+*$-F;6# F=F+FAF+*&*(F-F+F*F+F2F+F+*$-F;6#F=F+FAF+*&#F+F.F+*&*&F*F+FDF+F+*$-F;6 #F=F+FAF+FA*&#F+F.F+*&*&F/F+F2F+F+*$-F;6#F=F+FAF+FA*&*(F-F+F/F+FDF+F+* $-F;6#F=F+FAF+/-%\"yGF'*&,(*&%#FyGF+)F(F.F+F-*(F@F+--FT6#FbpF0F+F(F+F+ *&F@F+-FbpF0F+F+F+F@FA/-%\"zGF'*&,(*&%#FzGF+FgpF+F-*(F@F+--FT6#F`qF0F+ F(F+F+*&F@F+-F`qF0F+F+F+F@FA" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#R6#%\" tG6\"6$%)operatorG%&arrowGF&7%,8%#FxG\"\"\"*(#F-\"\"#F--%\"xG6#\"\"!F- -%$expG6#,$*&*&,&*$-%%sqrtG6#,&F-F-*&\"\"%F-%\"mGF-!\"\"F-F-F-F-F-9$F- F-FCFD#FDF0F-F-*(F/F-F1F--F66#,$*&*&,&F6#F@F-FDFD*&*(FCF-FVF-FHF-F-*$-F>6#F@F-FDF-*&*(F/F-F,F-F5F-F-*$-F> 6#F@F-FDF-*&#F-F0F-*&*&F,F-FHF-F-*$-F>6#F@F-FDF-FD*&#F-F0F-*&*&F1F-F5F -F-*$-F>6#F@F-FDF-FD*&*(F/F-F1F-FHF-F-*$-F>6#F@F-FDF-*&,(*&%#FyGF-)FEF 0F-F/*(FCF---FX6#%\"yGF3F-FEF-F-*&FCF--F]qF3F-F-F-FCFD*&,(*&%#FzGF-Fhp F-F/*(FCF---FX6#%\"zGF3F-FEF-F-*&FCF--FhqF3F-F-F-FCFDF&F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "rf(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7%,8%#FxG\"\"\"*(#F&\"\"#F&%#x0GF&-%$expG6#,$*&*&,&*$-% %sqrtG6#,&F&F&*&\"\"%F&%\"mGF&!\"\"F&F&F&F&F&%\"tGF&F&F9F:#F:F)F&F&*(F (F&F*F&-F,6#,$*&*&,&F2F&F&F:F&F;F&F&F9F:F(F&F&*&#F&F)F&*&F%F&F+F&F&F:* &#F&F)F&*&F%F&F>F&F&F:*&*(F9F&%$vx0GF&F+F&F&*$-F46#F6F&F:F:*&*(F9F&FLF &F>F&F&*$-F46#F6F&F:F&*&*(F(F&F%F&F+F&F&*$-F46#F6F&F:F&*&#F&F)F&*&*&F% F&F>F&F&*$-F46#F6F&F:F&F:*&#F&F)F&*&*&F*F&F+F&F&*$-F46#F6F&F:F&F:*&*(F (F&F*F&F>F&F&*$-F46#F6F&F:F&*&,(*&%#FyGF&)F;F)F&F(*(F9F&%$vy0GF&F;F&F& *&F9F&%#y0GF&F&F&F9F:*&,(*&%#FzGF&F[pF&F(*(F9F&%$vz0GF&F;F&F&*&F9F&%#z 0GF&F&F&F9F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "vf(t);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#7%,6*&*(%#x0G\"\"\",&*$-%%sqrtG6#,&F(F (*&\"\"%F(%\"mGF(!\"\"F(F(F(F(F(-%$expG6#,$*&*&F)F(%\"tGF(F(F1F2#F2\" \"#F(F(F1F2#F2F0*&**#F(F0F(F'F(,&F*F(F(F2F(-F46#,$*&*&F@F(F9F(F(F1F2#F (F;F(F(F1F2F(*&**F?F(%#FxGF(F)F(F3F(F(F1F2F(*&#F(F0F(*&*(FIF(F@F(FAF(F (F1F2F(F2*&**FFF(%$vx0GF(F)F(F3F(F(*$-F,6#F.F(F2F(*&**FFF(FPF(F@F(FAF( F(*$-F,6#F.F(F2F(*&#F(F0F(*&*(FIF(F)F(F3F(F(*&-F,6#F.F(F1F(F2F(F2*&#F( F0F(*&*(FIF(F@F(FAF(F(*&-F,6#F.F(F1F(F2F(F2*&**F?F(F'F(F)F(F3F(F(*&-F, 6#F.F(F1F(F2F(*&**F?F(F'F(F@F(FAF(F(*&-F,6#F.F(F1F(F2F(*&,&*&%#FyGF(F9 F(F(*&F1F(%$vy0GF(F(F(F1F2*&,&*&%#FzGF(F9F(F(*&F1F(%$vz0GF(F(F(F1F2" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "af(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7%,6*&*(%#x0G\"\"\"),&*$-%%sqrtG6#,&F(F(*&\"\"%F(%\"mGF (!\"\"F(F(F(F(\"\"#F(-%$expG6#,$*&*&F*F(%\"tGF(F(F2F3#F3F4F(F(*$)F2F4F (F3#F(\"\")*&**F?F(F'F(),&F+F(F(F3F4F(-F66#,$*&*&FDF(F;F(F(F2F3#F(F4F( F(*$F>F(F3F(*&#F(F@F(*&*(%#FxGF(F)F(F5F(F(*$F>F(F3F(F3*&#F(F@F(*&*(FPF (FCF(FEF(F(*$F>F(F3F(F3*&#F(F1F(*&*(%$vx0GF(F)F(F5F(F(*&-F-6#F/F(F2F(F 3F(F3*&**#F(F1F(FenF(FCF(FEF(F(*&-F-6#F/F(F2F(F3F(*&**F?F(FPF(F)F(F5F( F(*&-F-6#F/F(F>F(F3F(*&#F(F@F(*&*(FPF(FCF(FEF(F(*&-F-6#F/F(F>F(F3F(F3* &#F(F@F(*&*(F'F(F)F(F5F(F(*&-F-6#F/F(F>F(F3F(F3*&**F?F(F'F(FCF(FEF(F(* &-F-6#F/F(F>F(F3F(*&%#FyGF(F2F3*&%#FzGF(F2F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "read `fi g.m`:winpl():" }}{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "m:=1: x0:=0: vx0:=2: Fx:=0:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "vtitle:=`x(t), v(t), a(t)`:vxlab:=t:vylab:=``:p spl(`p1newpro.ps`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot (\{rf(t)[1],vf(t)[1],af(t)[1]\},t=0..15);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "#unassign('x(t)','y(t)','z(t)','x0','vx0' ,'y0','vy0','z0','vz0');" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Und m it dem parametrischen Plot ein Phasenportrait:" }}{PARA 0 "" 0 "" {TEXT -1 61 "pspl(`p2newpro.ps`):vtitle:=`v-x-Diagramm`:vxlab:=x:vylab :=v:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "plot([rf(t)[1],vf(t )[1],t=0..15]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "komma @oe.uni-tuebingen.de" }}}}{MARK "0 0 0" 15 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }