{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{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 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Out put" 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 0 }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 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "He lvetica" 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 2 2 0 1 }} {SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT 256 25 "Moderne Physik mit Mapl e " }}{PARA 258 "" 0 "" {TEXT 257 9 "PDF-Buch " }{URLLINK 17 "Moderne \+ Physik mit Maple" 4 "http://mikomma.de/fh/modphys.pdf" "" }}{PARA 258 "" 0 "" {TEXT -1 19 "Update auf Maple 10" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 13 "Kapitel 4.1.2" }}{PARA 258 " " 0 "" {TEXT -1 22 "Worksheet kino1_10.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "c International Thomson Publishing 1995 filename: fourw.m s" }}{PARA 0 "" 0 "" {TEXT -1 103 "Autor: Komma \+ Datum: 28.3.94" }}{PARA 0 "" 0 "" {TEXT -1 22 "Index:Wirkungsfunktion" }}{PARA 0 "" 0 "" {TEXT -1 64 "Thema: Wirkungsprinzip, schwaches Extremum der Wirkung sfunktion." }}{PARA 0 "" 0 "" {TEXT -1 34 "Wurf und harmonischer Oszil lator: " }}{PARA 0 "" 0 "" {TEXT -1 61 "N\344herungsl\366sung durch Be stimmung des schwachen Extremums der " }}{PARA 0 "" 0 "" {TEXT -1 75 " Wirkungsfunktion, wenn die Ortsfunktion als \"Fourierreihe\" angesetzt wird. " }}{PARA 0 "" 0 "" {TEXT -1 34 "Vergleich der Reihenentwicklun gen." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{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 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "T:=m/2*v^2 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG,$*(\"\"#!\"\"%\"mG\"\"\"% \"vGF'F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "v:=diff(x(t),t) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG-%%diffG6$-%\"xG6#%\"tGF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "L:=T-V(x(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,&*&#\"\"\"\"\"#F(*&%\"mGF()-%%diffG6$ -%\"xG6#%\"tGF3F)F(F(F(-%\"VG6#F0!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "S:=int(L,t=t0..t1);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"SG-%$intG6$,&*&#\"\"\"\"\"#F+*&%\"mGF+)-%%diffG6$-%\"xG6#%\"tGF6 F,F+F+F+-%\"VG6#F3!\"\"/F6;%#t0G%#t1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "H:=T+V(x(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" HG,&*&#\"\"\"\"\"#F(*&%\"mGF()-%%diffG6$-%\"xG6#%\"tGF3F)F(F(F(-%\"VG6 #F0F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "t0:=0:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "\334berlagerung von n Oberschwingungen (n >2) , Kurve durch (0|0) und (t1|x1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n:=6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "xx:=proc(t) local xl;" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "xl:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "for i to n do" }}{PARA 0 "" 0 "" {TEXT -1 71 "mit dem Cosinus bekommt man die Randbed. ohne gleichf. Bewegung herein." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "xl:=xl+a||i*sin(i*Pi*t/t1)+b||i*cos (i*Pi*t/t1); " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od; " }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "RETURN(xl);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 7 "" 1 "" {TEXT -1 60 "Warning, `i` is implicitly declared local to procedure `xx`\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xxGf*6#%\"tG6$%#xlG%\"iG6\"F+C%>8$ \"\"!?(8%\"\"\"F2%\"nG%%trueG>F.,(F.F2*&(%\"aGF1F2-%$sinG6#**F1F2%#PiG F29$F2%#t1G!\"\"F2F2*&(%\"bGF1F2-%$cosGF " 0 "" {MPLTEXT 1 0 6 "xx(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,:*&%#a1G\"\"\"-%$sinG6#*(%#PiGF&%\"tGF&%#t1G!\"\"F&F&* &%#b1GF&-%$cosGF)F&F&*&%#a2GF&-F(6#,$**\"\"#F&F+F&F,F&F-F.F&F&F&*&%#b2 GF&-F2F6F&F&*&%#a3GF&-F(6#,$**\"\"$F&F+F&F,F&F-F.F&F&F&*&%#b3GF&-F2F@F &F&*&%#a4GF&-F(6#,$**\"\"%F&F+F&F,F&F-F.F&F&F&*&%#b4GF&-F2FJF&F&*&%#a5 GF&-F(6#,$**\"\"&F&F+F&F,F&F-F.F&F&F&*&%#b5GF&-F2FTF&F&*&%#a6GF&-F(6#, $**\"\"'F&F+F&F,F&F-F.F&F&F&*&%#b6GF&-F2FhnF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "Zwei Koeffizienten (z.B. b1 und b2) lassen sich mit Hilfe der Bedingungen x(0)=0 und x(t1)=x1 durch die anderen Koeffizie nten ausdr\374cken: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "solb:=solve(\{xx(0)=0,xx(t 1)=x1\},\{b1,b2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solbG<$/%#b2 G,(%#b4G!\"\"%#b6GF**&\"\"#F*%#x1G\"\"\"F//%#b1G,(%#b5GF**&F-F*F.F/F*% #b3GF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x:=t->subs(solb,xx(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGf*6#%\"tG6\"6$%)operatorG%&arrowGF(-%%subsG6$% %solbG-%#xxG6#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,:*&%#a1G\"\"\"-%$sinG6#*(%#PiGF&%\"tGF&%#t1G!\"\"F&F&* &,(%#b5GF.*&\"\"#F.%#x1GF&F.%#b3GF.F&-%$cosGF)F&F&*&%#a2GF&-F(6#,$**F3 F&F+F&F,F&F-F.F&F&F&*&,(%#b4GF.%#b6GF.*&F3F.F4F&F&F&-F7F;F&F&*&%#a3GF& -F(6#,$**\"\"$F&F+F&F,F&F-F.F&F&F&*&F5F&-F7FGF&F&*&%#a4GF&-F(6#,$**\" \"%F&F+F&F,F&F-F.F&F&F&*&F@F&-F7FPF&F&*&%#a5GF&-F(6#,$**\"\"&F&F+F&F,F &F-F.F&F&F&*&F1F&-F7FYF&F&*&%#a6GF&-F(6#,$**\"\"'F&F+F&F,F&F-F.F&F&F&* &FAF&-F7F\\oF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "V(x);" }} {PARA 0 "" 0 "" {TEXT -1 5 "x(0);" }}{PARA 0 "" 0 "" {TEXT -1 44 "line ares Potential / qudratisches Potential:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "k:='k':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " V:=proc(x)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "m*g*x;" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "#1/2*k*x^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VGf*6#%\"xG6\"F(F(*(%\" mG\"\"\"%\"gGF+9$F+F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#g:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#t1:=2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "#S;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Ss:=simplify(S,power);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#SsG,$*,\"&Sa&!\"\"%\"mG\"\"\",ho**\"&+G&F*)%#PiG\"\" #F*%#x1GF*%#a5GF*F(**\"'s1aF*F.F*%#b3GF*%#a4GF*F(**\"&?R(F*F.F*%#a1GF* F1F*F***\"'cI8F*F.F*F1F*%#a3GF*F(**\"'?zLF*F.F*%#b5GF*%#a2GF*F***\"(++ #>F*F.F*F2F*%#b6GF*F***\"&o&HF*F.F*F9F*%#b4GF*F(**\"(o:E\"F*F.F*F?F*F6 F*F***\"'++))F*F.F*FFF*F2F*F(**\"'_F?F*F.F*F5F*%#a6GF*F(**\"&gp$F*F.F* F1F*F@F*F***\"')3t%F*F.F*F5F*F@F*F***\"%/&*F*F.F*F1F*FMF*F***\"(Kk-\"F *F.F*FFF*F " 0 "" {MPLTEXT 1 0 5 "x(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,:*&%#a1G\"\" \"-%$sinG6#*(%#PiGF&%\"tGF&%#t1G!\"\"F&F&*&,(%#b5GF.*&\"\"#F.%#x1GF&F. %#b3GF.F&-%$cosGF)F&F&*&%#a2GF&-F(6#,$**F3F&F+F&F,F&F-F.F&F&F&*&,(%#b4 GF.%#b6GF.*&F3F.F4F&F&F&-F7F;F&F&*&%#a3GF&-F(6#,$**\"\"$F&F+F&F,F&F-F. F&F&F&*&F5F&-F7FGF&F&*&%#a4GF&-F(6#,$**\"\"%F&F+F&F,F&F-F.F&F&F&*&F@F& -F7FPF&F&*&%#a5GF&-F(6#,$**\"\"&F&F+F&F,F&F-F.F&F&F&*&F1F&-F7FYF&F&*&% #a6GF&-F(6#,$**\"\"'F&F+F&F,F&F-F.F&F&F&*&FAF&-F7F\\oF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "Notwendige Bedingung f\374r schwaches Ex tremum: die partiellen Ableitungen der Wirkung nach den Formvariablen \+ m\374ssen verschwinden." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "sys:=seq(diff(Ss,a||j),j=1..n),seq( diff(Ss,b||j),j=3..n); # n>2" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$sys G6,,$*,\"&Sa&!\"\"%\"mG\"\"\",,*(\"&?R(F+)%#PiG\"\"#F+%#x1GF+F+*(\"&o& HF+F/F+%#b4GF+F)*(\"&?x#F+)F0\"\"$F+%#a1GF+F)*(\"'!)36F+%\"gGF+)%#t1GF 1F+F+*(\"&#zLF+F/F+%#b6GF+F)F+F?F)F0F)F),$*,F(F)F*F+,**(\"'?zLF+F/F+%# b5GF+F+*(\"&gp$F+F/F+F2F+F+*(\"')3t%F+F/F+%#b3GF+F+*(FF+F+*(\"'K'4(F+F/F+FBF+F+F+F?F)F0F) F),$*,F(F)F*F+,**(\"'s1aF+F/F+FMF+F)*(\"(o:E\"F+F/F+FHF+F+*(\"'?NWF+F8 F+%#a4GF+F)*(\"&%y9F+F/F+F2F+F+F+F?F)F0F)F),$*,F(F)F*F+,,*(\"&+G&F+F/F +F2F+F)*(\"(++#>F+F/F+FBF+F+*(\"'++))F+F/F+F5F+F)*(\"'+IpF+F8F+%#a5GF+ F)*(\"&w@#F+F=F+F>F+F+F+F?F)F0F)F),$*,F(F)F*F+,**(\"'_F?F+F/F+FMF+F)*( \"%/&*F+F/F+F2F+F+*(\"(#*H\\\"F+F/F+FHF+F)*(\"'?z**F+F8F+%#a6GF+F)F+F? F)F0F)F),$*,F(F)F*F+,.*(F[oF+F/F+F`oF+F)*(FepF+F/F+F\\qF+F)*(FLF+F/F+F OF+F+*(\"'+sFF+F8F+FMF+F)*(F7F+F8F+FHF+F)*(\"&gQ\"F+F8F+F2F+F)F+F?F)F0 F)F),$*,F(F)F*F+,.*(F4F+F/F+F:F+F)*(F[pF+F/F+F^pF+F)*(FVF+F/F+FYF+F+*( \"'+WbF+F8F+F5F+F)*(F(F+F8F+F2F+F+*(F " 0 "" {MPLTEXT 1 0 37 "#sys:=seq(diff(Ss,a.j),j=1..n); # n=2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "sol:=solve(\{sys\},\{a||(1.. n),b||(3..n)\}); #n>2" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solG<,/%#a 6G,$*.\"$v#\"\"\"\"$T%!\"\"%#x1GF+,(*&\".gh*fByqF+)%#PiG\"\"#F+F-\"/K) )3sV=NF+*&\"-v.;tfNF+)F3\"\"%F+F+F+F3F-,(*&\"/+/JI;o%*F+F2F+F-\"0;[:Po Rd%F+*&\".DJLRw*[F+F8F+F+F-F+/%#b3G,$*,\"$D\"F+\"#9F-F.F+,(*&\",Dhstk# F+F8F+F+*&\"-gdwJn^F+F2F+F-\"._F!e9@DF+F+F:F-F-/%#a5G,$*,\"#WF+\"&v$=F -,.*(\"/+]i[&\\3$F+)F3\"\"'F+F.F+F-*(\"0++_NEIr#F+F8F+F.F+F+*(\"0+GL)[ `)H$F+F2F+F.F+F+**\"0+%Q?bWlP[#Q7F+F8F+FgnF+FhnF+F+F+F3!\"$,(*&\"/+#>oUx_\"F+ F2F+F-*&\"-vVT!eE*F+F8F+F+\"/7Xuv&f0'F+F-F+/%#a2G,$*.FDF+\"$Z\"F-F.F+, (*&\"-DKOu)G%F+F8F+F+*&\"._v/\\wz(F+F2F+F-F5F+F+F3F-F:F-F+/%#a3G,$*,\" #?F+\"%B8F-,.*(\".+E#QS9CF+FUF+F.F+F-*(\".ob?/s()*F+F8F+F.F+F-*(FZF+F2 F+F.F+F+**\"0![!e9XqV\"F+F2F+FgnF+FhnF+F-*(F[oF+FgnF+FhnF+F+**\".v31)[ !3*F+F8F+FgnF+FhnF+F+F+F3F^oF_oF-F+/%#b6G,$*,\"#AF+\"#@F-,,*(\"-+;;oX! )F+F8F+F.F+F-**\",+5_VY#F+F2F+FgnF+FhnF+F+*(\",Dc`+h$F+FUF+F.F+F+*(\". %Q7XbCWF+F2F+F.F+F+*(\"-?6Y&RV#F+FgnF+FhnF+F-F+F3!\"#F_oF-F+/%#a1G,$*, \"$+\"F+F,F-,.*(\"/+ur%)HH5F+FUF+F.F+F+*(\"0s9oKeQo\"F+F8F+F.F+F-*(\"0 +cmwpqf'F+F2F+F.F+F+**\"0kg$4f_'p#F+F2F+FgnF+FhnF+F-*(\"1[g#Q\"[#)p5F+ FgnF+FhnF+F+**\"/v&4&y[M;F+F8F+FgnF+FhnF+F+F+F3F^oF_oF-F+/%#a4G,$*.\"# DF+\"#)*F-,(*&\"-v)4bo?)F+F8F+F+*&\"/!3!fC(H_\"F+F2F+F-\"/kw\"F+FUF+F.F+F+*(\"/ +3AKb2?F+F8F+F.F+F-*(\"/7*y'ov+#)F+F2F+F.F+F+**\",+Sm#\\fF+F2F+FgnF+Fh nF+F+*(\"-!ovR#\\aF+FgnF+FhnF+F-F+F3FarF_oF-F+" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 35 "#sol:=solve(\{sys\},\{a.(1..n)\}); #n=2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,:*&%#a1G\"\"\"-%$sinG6#*(%#PiGF&%\"tGF&%#t1G!\"\"F&F&* &,(%#b5GF.*&\"\"#F.%#x1GF&F.%#b3GF.F&-%$cosGF)F&F&*&%#a2GF&-F(6#,$**F3 F&F+F&F,F&F-F.F&F&F&*&,(%#b4GF.%#b6GF.*&F3F.F4F&F&F&-F7F;F&F&*&%#a3GF& -F(6#,$**\"\"$F&F+F&F,F&F-F.F&F&F&*&F5F&-F7FGF&F&*&%#a4GF&-F(6#,$**\" \"%F&F+F&F,F&F-F.F&F&F&*&F@F&-F7FPF&F&*&%#a5GF&-F(6#,$**\"\"&F&F+F&F,F &F-F.F&F&F&*&F1F&-F7FYF&F&*&%#a6GF&-F(6#,$**\"\"'F&F+F&F,F&F-F.F&F&F&* &FAF&-F7F\\oF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "L\366sung des Gleichungssystems in x(t) einsetzen:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "xs:=pro c() subs(sol,x(t)); end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xsGf*6 \"F&F&F&-%%subsG6$%$solG-%\"xG6#%\"tGF&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "xs();" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,:*&#\"$+ \"\"$T%\"\"\"**,.*(\"/+ur%)HH5F()%#PiG\"\"'F(%#x1GF(F(*(\"0s9oKeQo\"F( )F.\"\"%F(F0F(!\"\"*(\"0+cmwpqf'F()F.\"\"#F(F0F(F(**\"0kg$4f_'p#F(F8F( 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RR=5Fgz-Fiz6&F[[lF(F\\[lF(-%+AXESLABELSG6$Q\"t6\"Q!F\\el-%%VIEWG6$;F(F cz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "soly( );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"&\"\"\")%\"tG\"\"#F&!\" \"*&#\"#BF)F&F(F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "diff(V(y), y);" }}{PARA 0 "" 0 "" {TEXT -1 8 "V(x(t));" }}{PARA 0 "" 0 "" {TEXT -1 48 "Vergleich des Polynoms mit der Reihenentwicklung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(series(soly(),t,10));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#+'%\"tG$\"++++]6!\")\"\"\"$!\"&\"\"!\" \"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalf(series(xs(),t) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+/%\"tG$\"+9%G/:\"!\")\"\"\"$!+< kx'3&!\"*\"\"#$\"*(=a<\\F+\"\"$$!*B\"RUqF+\"\"%$!*T8BB#F'\"\"&-%\"OG6# F(\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 285 "Anmerkungen: Der L \366sungsansatz wird mit der Periode t1 gemacht. Deshalb erh\344lt man auch bei quadratischem Potential (Oszillator) nicht die exakte L\366s ung, man kann aber die Reihenentwicklungen vergleichen. Nat\374rlich k ann man mit t1 (im Argument der Winkelfunktionen) experimentieren ... " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "komma@oe.uni-tuebingen.de" }}}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }