{VERSION 5 0 "SUN SPARC SOLARIS" "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 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 "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 "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 280 "bisect := proc(f, i nterval, epsilon)\n local xlo, xhi, mid;\n xlo := interval[1];\n xh i := interval[2];\n while( xhi - xlo > epsilon ) do\n mid := (xlo \+ + xhi)/2;\n if ( f(mid) < 0 ) then\n xlo := mid;\n else\n \+ xhi := mid;\n fi; \n od;\n\n return([xlo,xhi]);\nend;" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'bis ectGf*6%%\"fG%)intervalG%(epsilonG6%%$xloG%$xhiG%$midG6\"F.C&>8$&9%6# \"\"\">8%&F36#\"\"#?(F.F5F5F.29&,&F7F5F1!\"\"C$>8&,&F1#F5F:*&FDF5F7F5F 5@%2-9$6#FB\"\"!>F1FB>F7FBO7$F1F7F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "mid:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$midG\"\" &" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "bisect(x->x^2-2, [0, 3 ], 0.0001);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$#\"&pJ#\"&%Q;#\"&Tj% \"&oF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "mid;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "bisect(x->x^2-2, [5, 7.0], 0.0001);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"\"&$\"+N51+]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 415 "bisect := proc(f, interval, epsilon)\n local xlo, xhi, mid;\n x lo := interval[1];\n xhi := interval[2];\n if ( sign(f(xlo)) = sign( f(xhi))) then\n print( xlo, \"and\", xhi, \"don't bracket a zero: \", [f(xlo), f(xhi)]);\n return();\n fi;\n while( xhi - xlo > ep silon ) do\n mid := (xlo + xhi)/2;\n if ( f(mid) < 0 ) then\n \+ xlo := mid;\n else\n xhi := mid;\n fi; \n od;\n\n r eturn([xlo,xhi]);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " bisect(x->x^2-2, [5, 7.0], 0.0001);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 '\"\"&Q$and6\"$\"#q!\"\"Q6don't~bracket~a~zero:F%7$\"#B$\"%+Z!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Back to \+ the glider:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 596 "xhit:= proc ( theta0, v0 )\n local sol;\n global R;\n sol:=dsolve(\n \+ \{diff(theta(t),t) = piecewise( y(t)>0, (v(t)^2 - cos(theta(t)))/v(t ), 0),\n diff(v(t),t) = piecewise( y(t)>0, -sin(theta(t) ) - R*v(t)^2 , 0),\n diff(x(t),t) = piecewise( y(t)>0 , v(t)*cos(theta(t)), 0),\n diff(y(t),t) = pi ecewise( y(t)>0, v(t)*sin(theta(t)), 0),\n diff(T( t),t) = piecewise( y(t)>0, 1, 0),\n \+ v(0)=v0, theta(0)=theta0, x(0)=0, y(0)=1, T(0)=0\}, numeric); \n return(subs(sol(20),x(t))); \nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "R:=0.2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG$\"\" #!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "xhit(0, 1.2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3WK?,KJ\\Bj!#<" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "R:=0.01;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"RG$\"\"\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "xhit(0, 1.2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3c1%Q!RYYn>!#;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "THIS IS A LIE! WRONG WRONG WORNG !\033" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 633 "xhit:= proc( theta0, v0 )\n local sol;\n global \+ R, hitvalues;;\n sol:=dsolve(\n \{diff(theta(t),t) = piecew ise( y(t)>0, (v(t)^2 - cos(theta(t)))/v(t), 0),\n diff(v(t),t ) = piecewise( y(t)>0, -sin(theta(t)) - R*v(t)^2 , 0),\n \+ diff(x(t),t) = piecewise( y(t)>0, v(t)*cos(theta(t)), \+ 0),\n diff(y(t),t) = piecewise( y(t)>0, v(t)*sin(the ta(t)), 0),\n diff(T(t),t) = piecewise( y(t)> 0, 1, 0),\n v(0)=v0, theta(0)=the ta0, x(0)=0, y(0)=1, T(0)=0\}, numeric);\n hitvalues:=sol(20);\n r eturn(subs(hitvalues,x(t))); \nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "xhit(0, 1.2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3 c1%Q!RYYn>!#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "hitvalues; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7(/%\"tG$\"#?\"\"!/-%\"TG6#F%F&/-% &thetaGF,$!3=C&=E`7pH\"!#>/-%\"vGF,$\"3EQd'oO`fU)!#=/-%\"xGF,$\"3c1%Q! RYYn>!#;/-%\"yGF,$\"3s$4yZWkb:\"!#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 777 "xhit:= proc( theta0, v0 )\n local sol, flytime;\n \+ global R, hitvalues;\n flytime:=10;\n sol:=dsolve(\n \{d iff(theta(t),t) = piecewise( y(t)>0, (v(t)^2 - cos(theta(t)))/v(t), 0 ),\n diff(v(t),t) = piecewise( y(t)>0, -sin(theta(t)) - \+ R*v(t)^2 , 0),\n diff(x(t),t) = piecewise( y(t)>0, v( t)*cos(theta(t)), 0),\n diff(y(t),t) = piecew ise( y(t)>0, v(t)*sin(theta(t)), 0),\n diff(T(t),t ) = piecewise( y(t)>0, 1, 0),\n \+ v(0)=v0, theta(0)=theta0, x(0)=0, y(0)=1, T(0)=0\}, numeric);\n \+ do \n hitvalues:=sol(flytime);\n if (subs(hitvalues,y(t)) <0 ) then\n return(subs(hitvalues,x(t)));\n else\n \+ flytime:=flytime+10;\n fi \n od;\nend:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "xhit(0, 1.2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3$)Q@86dS$=\"!#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "R ; hitvalues;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"!\"#" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7(/%\"tG$\"$?\"\"\"!/-%\"TG6#F%$\"3#H%Rm-))p !>\"!#:/-%&thetaGF,$!3gm!e9dE?q&!#>/-%\"vGF,$\"3)[:1fFY%45!# " 0 "" {MPLTEXT 1 0 8 "R:=0.2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" RG$\"\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "xhit(0, 1. 2, 0.01);\nxhit(0, 2.0, 0.01);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3 WK?,KJ\\Bj!#<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"39eQ)Q_h66)!#<" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "bisect(v->xhit(0,v)-8.0, [1 .2, 2.0], 0.00001);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+kF$[$>!\" *$\"+o)Q[$>F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "23 0 0" 16 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }