{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 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 0 } 3 3 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 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT -1 10 "P\370\355klad 3." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 72 "Ur\350et\354 t\354\236i\232t\354 dr\341tu (homogen n\355ho) ve tvaru jednoho oblouku cykloidy : " }}{PARA 0 "" 0 "" {TEXT -1 17 " " }{XPPEDIT 18 0 "phi = a*(t-sin(t)),psi = a*(1-cos(t));" "6$/%$phiG*&%\"aG\"\"\",&%\"tGF'-%$sinG6#F)!\"\"F'/% $psiG*&F&F',&F'F'-%$cosG6#F)F-F'" }{TEXT -1 26 " , t n\341le\236\355 \+ do intervalu " }{XPPEDIT 18 0 "<0,2*Pi>;" "6#-%7rtable/ConstructColumn G6$\"\"!6#*&\"\"#\"\"\"%#PiGF*" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Nejprve k\370ivku nakresl\355me , " }{XPPEDIT 18 0 "a = 1;" "6#/%\"aG\"\"\"" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([t-sin(t),1-cos(t),t=0..2*Pi],scaling=constraine d);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Statick\351 momenty " }{XPPEDIT 18 0 "S[x],S[y];" "6$&%\"SG6#% \"xG&F$6#%\"yG" }{TEXT -1 27 " se po\350\355taj\355 dle vzorc\371 : " }{XPPEDIT 18 0 "S[x] = rho*Int(psi(t)*sqrt(phi(t)^`\2642`+psi(t)^` \2642`),t = t[1] .. t[2]);" "6#/&%\"SG6#%\"xG*&%$rhoG\"\"\"-%$IntG6$*& -%$psiG6#%\"tGF*-%%sqrtG6#,&)-%$phiG6#F2%#|_v2GF*)-F06#F2F;F*F*/F2;&F2 6#F*&F26#\"\"#F*" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 " \+ \+ " }{XPPEDIT 18 0 "S[y] = rho*Int(phi(t)*sqrt(phi(t)^`\2642`+psi(t)^` \2642`),t = t[1] .. t[2]);" "6#/&%\"SG6#%\"yG*&%$rhoG\"\"\"-%$IntG6$*& -%$phiG6#%\"tGF*-%%sqrtG6#,&)-F06#F2%#|_v2GF*)-%$psiG6#F2F:F*F*/F2;&F2 6#F*&F26#\"\"#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "ffi:=a* (t-sin(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ffiG*&%\"aG\"\"\",&% \"tGF'-%$sinG6#F)!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "ppsi:=a*(1-cos(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ppsiG*&%\"a G\"\"\",&F'F'-%$cosG6#%\"tG!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "derfi:=Diff(a*(t-sin(t)),t)=diff(a*(t-sin(t)),t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&derfiG/-%%DiffG6$*&%\"aG\"\"\",&%\" tGF+-%$sinG6#F-!\"\"F+F-*&F*F+,&F+F+-%$cosGF0F1F+" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 50 "derpsi:=Diff(a*(1-cos(t)),t)=diff(a*(1-cos(t )),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'derpsiG/-%%DiffG6$*&%\"aG \"\"\",&F+F+-%$cosG6#%\"tG!\"\"F+F0*&F*F+-%$sinGF/F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "odmoc:=sqrt(rhs(derfi)^2+rhs(derpsi)^2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&odmocG*$-%%sqrtG6#,&*&)%\"aG\" \"#\"\"\"),&F.F.-%$cosG6#%\"tG!\"\"F-F.F.*&F+F.)-%$sinGF3F-F.F.F." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "odmoc:=simplify(odmoc);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&odmocG*&-%%sqrtG6#\"\"#\"\"\"-F'6#, $*&)%\"aGF)F*,&!\"\"F*-%$cosG6#%\"tGF*F*F2F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "odmoc:=expand(odmoc);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&odmocG*&-%%sqrtG6#\"\"#\"\"\"-F'6#,&*$)%\"aGF)F*F**& F/F*-%$cosG6#%\"tGF*!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "SX:=rho*Int(ppsi*odmoc,t=0..2*Pi)=rho*int(ppsi*odmoc,t=0..2*Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SXG/*&%$rhoG\"\"\"-%$IntG6$**%\"a GF(,&F(F(-%$cosG6#%\"tG!\"\"F(-%%sqrtG6#\"\"#F(-F56#,&*$)F-F7F(F(*&F " 0 "" {MPLTEXT 1 0 12 "assume(a>0);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 22 "Sx:=simplify(rhs(SX));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#SxG,$*&%$rhoG\"\"\")%#a|irG\"\"#F(#\"#K\"\"$" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Hmotnost se po\350\355t\341 podle \+ vzorce " }{XPPEDIT 18 0 "m = Int(sqrt(phi(t)^`\2642`+psi(t)^`\2642` ),t = t[1] .. t[2]);" "6#/%\"mG-%$IntG6$-%%sqrtG6#,&)-%$phiG6#%\"tG%#| _v2G\"\"\")-%$psiG6#F0F1F2/F0;&F06#F2&F06#\"\"#" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 47 "m:=Int(odmoc,t=0..2*Pi)=int(odmoc,t=0..2*Pi); \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG/-%$IntG6$*&-%%sqrtG6#\"\"# \"\"\"-F+6#,&*$)%#a|irGF-F.F.*&F3F.-%$cosG6#%\"tGF.!\"\"F./F9;\"\"!,$% #PiGF-,$F4\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x[t]:=Pi *a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#%\"tG*&%#PiG\"\"\"%#a| irGF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y[t]:=Sx/rhs(m);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#%\"tG,$*&%$rhoG\"\"\"%#a|ir GF+#\"\"%\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "21 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }