{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 "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 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 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 Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ps:=(U,V)->U[1]*V[1]+U[ 2]*V[2]+U[3]*V[3]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "pv:=( U,V)->[U[2]*V[3]-U[3]*V[2],U[3]*V[1]-U[1]*V[3],U[1]*V[2]-U[2]*V[1]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "M:=[f(t),g(t),h(t)]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "T:=diff(M,t):A:=diff(T,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "B:=simplify(pv(T,A)):Nc:= simplify(pv(B,T)):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "tri\350dre \+ fr\351net non norm\351" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "(T ,Nc,B);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%7%-%%diffG6$-%\"fG6#%\"tGF* -F%6$-%\"gGF)F*-F%6$-%\"hGF)F*7%,**&)F+\"\"#\"\"\"-F%6$F'-%\"$G6$F*F7F 8F8*(F+F8-F%6$F-F;F8F$F8!\"\"*(-F%6$F1F;F8F/F8F$F8FA*&)F/F7F8F9F8F8,** (F+F8FCF8F/F8FA*(F+F8F$F8F9F8FA*&FFF8F?F8F8*&F?F8)F$F7F8F8,**&F6F8FCF8 F8*(F+F8F/F8F?F8FA*&FCF8FLF8F8*(F/F8F$F8F9F8FA7%,&*&F+F8FCF8F8*&F/F8F? F8FA,&*&F$F8FCF8FA*&F/F8F9F8F8,&*&F$F8F?F8F8*&F+F8F9F8FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "N:=[0,0,1]:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "costheta2:=ps(B,N)^2/ps(B,B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*costheta2G*&,&*&-%%diffG6$-%\"fG6#%\"tGF.\"\"\" -F)6$-%\"gGF--%\"$G6$F.\"\"#F/F/*&-F)6$F2F.F/-F)6$F+F4F/!\"\"F7,(*$),& *&F9F/-F)6$-%\"hGF-F4F/F/*&-F)6$FEF.F/F0F/F=F7F/F/*$),&*&F(F/FCF/F=*&F HF/F;F/F/F7F/F/*$)F&F7F/F/F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "G:=pv(N,T);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG7%,$-%%diff G6$-%\"gG6#%\"tGF-!\"\"-F(6$-%\"fGF,F-\"\"!" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 15 "tri\350dre darboux" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(T,G,N);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7%-%%diffG 6$-%\"fG6#%\"tGF*-F%6$-%\"gGF)F*-F%6$-%\"hGF)F*7%,$F+!\"\"F$\"\"!7%F6F 6\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ds2:=ps(T,T);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ds2G,(*$)-%%diffG6$-%\"fG6#%\"tGF. \"\"#\"\"\"F0*$)-F)6$-%\"gGF-F.F/F0F0*$)-F)6$-%\"hGF-F.F/F0F0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Tvrai:=expand(T/sqrt(ds2)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&TvraiG7%*&-%%diffG6$-%\"fG6#%\" tGF-\"\"\",(*$)F'\"\"#F.F.*$)-F(6$-%\"gGF,F-F2F.F.*$)-F(6$-%\"hGF,F-F2 F.F.#!\"\"F2*&F5F.F/F?*&F;F.F/F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "dphi2:=simplify(ps(diff(Tvrai,t),diff(Tvrai,t)));" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%&dphi2G*&,4*&)-%%diffG6$-%\"gG6#%\"t GF/\"\"#\"\"\")-F*6$-%\"hGF.-%\"$G6$F/F0F0F1F1*&F(F1)-F*6$-%\"fGF.F7F0 F1F1*,F0F1F)F1F3F1-F*6$F5F/F1-F*6$F,F7F1!\"\"*,F0F1F)F1-F*6$F>F/F1F " 0 "" {MPLTEXT 1 0 15 "Rc2:=ds2/dphi2;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$Rc2G*&,(*$)-%%diffG6$-%\"fG6#%\"tGF/\"\"#\"\"\"F1*$) -F*6$-%\"gGF.F/F0F1F1*$)-F*6$-%\"hGF.F/F0F1F1\"\"$,4*&F3F1)-F*6$F<-%\" $G6$F/F0F0F1F1*&F3F1)-F*6$F,FDF0F1F1*,F0F1F4F1FBF1F:F1-F*6$F6FDF1!\"\" *,F0F1F4F1F)F1FIF1FLF1FN*&FAF1F(F1F1*,F0F1FBF1F:F1F)F1FIF1FN*&F9F1FHF1 F1*&F9F1)FLF0F1F1*&F(F1FTF1F1FN" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Rcg2:=simplify(Rc2/costheta2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Rcg2G*&,(*$)-%%diffG6$-%\"fG6#%\"tGF/\"\"#\"\"\"F1*$)-F*6$-% \"gGF.F/F0F1F1*$)-F*6$-%\"hGF.F/F0F1F1\"\"$,&*&F)F1-F*6$F6-%\"$G6$F/F0 F1!\"\"*&F4F1-F*6$F,FCF1F1!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f,g:=t->cos(t),t->sin(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> 6$%\"fG%\"gG6$f*6#%\"tG6\"6$%)operatorG%&arrowGF+-%$cosG6#9$F+F+F+f*F) F+F,F+-%$sinGF1F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "si mplify(Rcg2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),(*$)-%$sinG6#%\"t G\"\"#\"\"\"F-*$)-%$cosGF*F,F-F-*$)-%%diffG6$-%\"hGF*F+F,F-F-\"\"$F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "20 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }