{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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 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 }{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 0 "" 0 "" {TEXT -1 289 "Last time, we saw we coul d augment our phugoid (v, theta) differential equations by adding equa tions for (x,y), then plot either (v, theta) as before, or (x,y). Tod ay I'll first record a way to plot these two graphs side by side, for \+ easier comparision.\n\nFirst, define the new 4-D system:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 203 "\nxphug:=[ diff(theta(t),t) = (v(t)^2-cos(theta(t) ))/v(t),\n diff(v(t),t) = -sin(theta(t)) - R*v(t)^2,\n \+ diff(x(t),t) = v(t)*cos(theta(t)), \n diff(y(t),t) = v(t)*si n(theta(t)) ]; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&xphugG7&/-%%di ffG6$-%&thetaG6#%\"tGF-*&,&*$)-%\"vGF,\"\"#\"\"\"F5-%$cosG6#F*!\"\"F5F 2F9/-F(6$F2F-,&-%$sinGF8F9*&\"\"$F5F1F5F9/-F(6$-%\"xGF,F-*&F2F5F6F5/-F (6$-%\"yGF,F-*&F2F5F>F5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Next w e choose an R value:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "R:=.1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"RG$\"\"\"!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "Now we use commands display and array to do the \+ side-by-side graphs\nthe syntax is: display( array( [plot1, plot2])); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(plots): with(DEtoo ls):\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords \+ has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 465 "display( array([ \n DEplo t(xphug, [theta,v,x,y],\n t=0...20, theta=-Pi....7, v=0.01... 3, \n x=-1..5, y=0....3, \n [[v(0)=1.5, theta(0)=0 , x(0)=0, y(0)=2]],\n stepsize=0.1, scene=[theta,v], linecolo r=black), \n DEplot(xphug, [theta,v,x,y],\n t=0...20, theta =-Pi....7, v=0.01...3, \n x=-1..5, y=0....3, \n [[ v(0)=1.5, theta(0)=0, x(0)=0, y(0)=2]],\n stepsize=0.1, scene =[x,y], linecolor=black)\n]));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6L-%'CURVESG6'7$7$$\")m`p\\!\")\"#57$F(!#57$7$F-F-7$F +F-7$7$\"#?F+7$F3F-7$F47$\"#SF--%'LEGENDG6#QB__never_display_this_lege nd_entry6\"-F$6.7$7$$!+LxJ#\\*!\"*$!$v*!\"#7$FA$!%D5FF7$7$$!+-1cihFCFD 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