{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 256 "Times New Roman CE" 1 12 0 0 0 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Century Schoolbook" 1 10 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 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 "" 11 12 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "" 1 11 0 0 128 1 2 1 2 0 0 0 0 0 0 }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 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 70 "Pokus o je dnoduch\375 bal\355k pro pr\341ci s Lagrangeov\375mi rovnicemi 2. druh u " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 209 "DT:=proc(Z,x)\n loca l xx,xx1,xx2,dzdt,i;\n dzdt:=diff(Z,t);\n for i from 1 to nops(x) do\n xx:=x[i];\n xx1:=cat(x[i],_);\n xx2:=cat(x[i],__);\n dzdt:=dzdt+d iff(Z,xx)*xx1+diff(Z,xx1)*xx2;\n od;\n RETURN (dzdt);\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DTGR6$%\"ZG%\"xG6'%#xxG%$xx1G%$xx2G%%dzdt G%\"iG6\"F/C%>8'-%%diffG6$9$%\"tG?(8(\"\"\"F:-%%nopsG6#9%%%trueGC&>8$& F>6#F9>8%-%$catG6$FC%\"_G>8&-FH6$FC%#__G>F2,(F2F:*&-F46$F6FBF:FFF:F:*& -F46$F6FFF:FLF:F:-%'RETURNG6#F2F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "LR:=proc(L,x) \n local qi,qi_,i,LL;\n LL:=\{\};\n fo r i from 1 to nops(x) do\n qi:=x[i];qi_:=cat(qi,_);\n LL:=\{op(LL),D T(diff(L,qi_),x)-diff(L,qi)=0\};\n od;\n RETURN (LL);\nend;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LRGR6$%\"LG%\"xG6&%#qiG%$ qi_G%\"iG%#LLG6\"F.C%>8'<\"?(8&\"\"\"F5-%%nopsG6#9%%%trueGC%>8$&F96#F4 >8%-%$catG6$F=%\"_G>F1<$-%#opG6#F1/,&-%#DTG6$-%%diffG6$9$FAF9F5-FQ6$FS F=!\"\"\"\"!-%'RETURNGFJF.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 303 "L2H:=proc(L,x) \n local qi,qi_,i,LL,LL_,iLL,H;\n H:=-L;LL:=\{ \};LL_:=\{\};\n for i from 1 to nops(x) do\n qi:=x[i];qi_:=cat(qi,_); \n p.i:=diff(L,qi_);\n LL_:=\{op(LL_),qi_\};\n LL:=\{op(LL),cat(p,q i)=p.i\};\n H:=H+diff(L,qi_)*qi_;\n od;\n iLL:=solve(LL,LL_);#print(i LL); \n RETURN(expand(simplify(subs(iLL,H))));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "#NASLEDUJICI UPRAVA dsolve SE HODI PRO RY CHLE POUZITI " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 726 "ddsolve:= proc()\n local F,f,ff,t,f0,op ts,i,R,n,S1,S2;\n if (nargs<3) then ERROR(\"Not enouh parameters in d dsolve\"); fi; \n F := args[1]; if not type(F,set) then F:=\{F\}; fi; \n ff := args[2]; if not type(ff,set) then ff:=\{ff\}; fi;\n t := ar gs[3];\n n:=nops(ff);\n f0:= \{\}; \n opts:=\{\};\n for i from 4 t o nargs do\n if (type(args[i],set(equation))) \n then f0:=\{op(f 0),op(args[i])\};\n else opts:=\{op(opts),args[i]\}; \n fi;\n o d;\n S1:=\{\};S2:=\{\};\n for f in ff do\n S1:=\{op(S1),cat(f,__) = diff(f(t),t,t),cat(f,_)=diff(f(t),t),f=f(t)\};\n S2:=\{op(S2),ca t(f,_)=D(f)\};\n od;\n R:=\{op(subs(S1,F)),op(subs(S2,f0))\};\n if \+ (nops(opts)>0) then RETURN(dsolve(R,map(f->f(t),ff),op(opts))); fi;\n \+ dsolve(R,map(f->f(t),ff));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "LR(x_^2 /2+y_^2/2-V(x),\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/,&%$x__ G\"\"\"-%%diffG6$-%\"VG6#%\"xGF.F'\"\"!/%$y__GF/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " LL:=1/2*m*(a/2)^2*psi_^2+1/2*(m*a^2/12)*psi_^2-m*g*(a/2)*cos(psi);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LLG,&*(%\"mG\"\"\")%\"aG\"\"#\"\"\" )%%psi_GF+F,#F(\"\"'**F'F,%\"gGF(F*F(-%$cosG6#%$psiGF(#!\"\"F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "L2H(LL,\{psi\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&*$)%%ppsiG\"\"#\"\"\"F)*&%\"mG\"\"\")%\" aG\"\"#F)!\"\"#\"\"$F(**F+\"\"\"%\"gGF4F.F4-%$cosG6#%$psiGF4#F4F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "EE:=1/2*m*(a/2)^2*psi_^2+1/2 *(m*a^2/12)*psi_^2+m*g*(a/2)*cos(psi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#EEG,&*(%\"mG\"\"\")%\"aG\"\"#\"\"\")%%psi_GF+F,#F(\"\"'**F'F, %\"gGF(F*F(-%$cosG6#%$psiGF(#F(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "E1:=simplify(subs(\{psi_=0,psi=arccos(h/a)\},EE));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#E1G,$*(%\"mG\"\"\"%\"gGF(%\"hGF(#F (\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "E2:=simplify(subs (\{psi_=v/a,psi=Pi/2\},EE));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#E2G ,$*&%\"mG\"\"\")%\"vG\"\"#\"\"\"#F(\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(E1=E2,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*& -%%sqrtG6#\"\"$\"\"\"-F%6#*&%\"gG\"\"\"%\"hGF-F(,$F#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "LK:=1/2*r_^2+1/2*r^2*phi_^2+M/r;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LKG,(*$)%#r_G\"\"#\"\"\"#\"\"\"F)* &)%\"rGF)F*)%%phi_GF)F*F+*&%\"MGF*F/!\"\"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "PRK:=LR(LK,\{r,phi\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PRKG<$/,(%$r__G\"\"\"*&%\"rGF))%%phi_G\"\"#\"\"\"!\" \"*&%\"MGF/*$)F+\"\"#F/!\"\"F)\"\"!/,&*(F+F/F-F)%#r_GF)F.*&)F+F.F/%&ph i__GF)F)F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "ddsolve(PRK, \{r,phi\},t,\{r(0)=R/(1+epsilon),r_( 0)=0,phi(0)=0,phi_(0)=Omega\},typ e=series);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<$/-%\"rG6#%\"tG++F(*&% \"RG\"\"\",&\"\"\"F.%(epsilonGF.!\"\"\"\"!,$*&,,*&)F+\"\"$F,)%&OmegaG \"\"#F,F.%\"MG!\"\"*&F;F.F/F.!\"$*&F;F,)F/F:F,F>*&F;F,)F/F7F,F \+ " 0 "" {MPLTEXT 1 0 54 "subs(r_=diff(R/(1+epsilon*cos(phi)),phi)*phi_, PRK[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*&*,%\"rG\"\"\")%%phi_G \"\"#\"\"\"%\"RGF(%(epsilonGF,-%$sinG6#%$phiGF(F,*$),&F(F(*&F.F(-%$cos GF1F(F(\"\"#F,!\"\"F+*&)F'F+F,%&phi__GF(F(\"\"!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "UR:=subs(r=R/(1+epsilon*cos(phi)),%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#URG/,&*&**)%\"RG\"\"#\"\"\")%%phi_G F+F,%(epsilonGF,-%$sinG6#%$phiG\"\"\"F,*$),&F4F4*&F/F4-%$cosGF2F4F4\" \"$F,!\"\"F+*&*&F)F,%&phi__GF4F,*$)F7\"\"#F,F " 0 "" {MPLTEXT 1 0 55 "ddsolve(UR,phi,t,\{phi(0)=0,phi_(0) =Omega\},type=series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$phiG6#% \"tG++F'%&OmegaG\"\"\",$*&*&)F)\"\"$\"\"\"%(epsilonG\"\"\"F0,&F2F2F1F2 !\"\"#!\"\"F/\"\"$,$*&*()F)\"\"&F0F1F0,&F2F2F1\"#7F2F0*$)F3\"\"#F0F4#F 2\"#g\"\"&-%\"OG6#F2\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 77 "ddsolve(\{y__+y=0,x__=y\},\{y,x\},t,\{y_(0)=0, y(0)=1,x_(0)=0,x(0)=0\},type=series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"xG6#%\"tG+)F(#\"\"\"\"\"#\"\"##!\"\"\"#C\"\"%-%\"OG6#F+\"\"' /-%\"yGF'++F(F+\"\"!#F/F,\"\"##F+F0\"\"%F2\"\"'" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 52 "ddsolve(\{y__+y=0\},y,t,\{y_(0)=0,y(0)=1\},typ e=series);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"tG++F'\"\"\" \"\"!#!\"\"\"\"#\"\"##F)\"#C\"\"%-%\"OG6#F)\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }