{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" 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "restart;# problem 1: let k=EA/d ux=uc_x ad uy=ub_y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "V:=k*uy^2/2/5/sqrt(5)+k*(uy-ux)^2/4/sqrt(2)-px*ux-py*uy;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,***\"#]!\"\"%\"kG\"\"\"%#uyG\" \"#\"\"&#F*F,F***\"\")F(F)F*,&F+F*%#uxGF(F,F,F.F**&%#pxGF*F2F*F(*&%#py GF*F+F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "e1:=diff(V,ux) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G,&**\"\"%!\"\"%\"kG\"\"\",& %#uyGF*%#uxGF(F*\"\"##F*F.F(%#pxGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "e2:=diff(V,uy);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #e2G,(**\"#D!\"\"%\"kG\"\"\"%#uyGF*\"\"&#F*\"\"#F***\"\"%F(F)F*,&F+F*% #uxGF(F*F.F-F*%#pyGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "so ls:=solve(\{e1,e2\},\{ux,uy\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%% solsG<$/%#uyG,$**\"\"&\"\"\"F*#F+\"\"#,&%#pxGF+%#pyGF+F+%\"kG!\"\"F+/% #uxG,$**F*F2F*F,,(*&\"#DF+F/F+F+*&F9F+F0F+F+**F-F+F-F,F*F,F/F+F+F+F1F2 F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "assign(sols);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "px:=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#pxG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "ux;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"&\"\"\"F%#F&\"\"#%#p yGF&%\"kG!\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "uy;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"&\"\"\"F%#F&\"\"#%#pyGF&%\"kG! \"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "restart;#prob 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "C:=fsolve((cosh(c)-1)/c/2 =1/4,c=0..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG$\"+P>@3$*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "L:=d*sinh(C)/C;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG,$*&$\"+:6z]6!\"*\"\"\"%\"dGF*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "T0:=w*d*cosh(C)/C/2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T0G,$*($\"+S4gry!#5\"\"\"%\"wGF*%\" dGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "theta0:=arctan(si nh(C));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'theta0G$\"+!z=v>)!#5" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Ts:=T0*cos(theta0)/sin(Pi/6 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#TsG,$*($\"+)=?V2\"!\"*\"\"\"% \"wGF*%\"dGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "F:=T0*si n(theta0)+Ts*cos(Pi/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,&*($ \"+rb&Rv&!#5\"\"\"%\"wGF*%\"dGF*F***$\"+S4gr`F)F*F+F*F,F*\"\"$#F*\"\"# F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*($\"+KTy0:!\"*\"\"\"%\"wGF(%\"dGF(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "restart;#problem 3" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "e1:=Ax=-Bx;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e1G/%#AxG,$%#BxG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "e2:=Ay+By=P;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#e2G/,&%#AyG\"\"\"%#ByGF(%\"PG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "e3:=-P*d/4-Bx*h+By*d/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e3G,(*(\"\"%!\"\"%\"PG\"\"\"%\"dGF*F(*&%#BxGF*%\"hGF*F(*(\"\" #F(%#ByGF*F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "e4:=Bx= Cx;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e4G/%#BxG%#CxG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "e5:=Cy=By;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#e5G/%#CyG%#ByG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "e6:=Cx*h+Cy*d/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#e6G,&*&%#CxG\"\"\"%\"hGF(F(*(\"\"#!\"\"%#CyGF(%\"dGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "solve(\{e1,e2,e3,e4,e5,e6\},\{Ax,Ay ,Bx,By,Cx,Cy\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(/%#CxG,$**\"\")! \"\"%\"hGF)%\"PG\"\"\"%\"dGF,F)/%#CyG,$*&\"\"%F)F+F,F,/%#AyG,$*(\"\"$F ,F2F)F+F,F,/%#ByGF0/%#BxGF&/%#AxG,$**F(F)F*F)F+F,F-F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }