{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{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 -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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Map le Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 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 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 32 "setoptions(scaling=constrained):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 12 "The Cycloid\n" }{TEXT -1 169 "We shall d emonstrate a cycloid being generated by a circle rolling without slipp ing on a line. First, we define functions needed to describe the cyclo id parametrically. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "x := t -> t \+ - sin(t);\ny := t -> 1 - cos(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"xGR6#%\"tG6\"6$%)operatorG%&arrowGF(,&9$\"\"\"-%$sinG6#F-!\"\"F(F(F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yGR6#%\"tG6\"6$%)operatorG%&ar rowGF(,&\"\"\"F--%$cosG6#9$!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Next some animation. We create an animation of a circle with a spoke, and move it along the x-axis from 0 to " }{XPPEDIT 18 0 "4*Pi" "6#*&\"\"%\"\"\"%#PiGF%" }{TEXT -1 51 ". The animation is sa ved in a variable named `a1'." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "a 1 := animate( \{[u-sin(t), 1-cos(t), t=0..2*Pi],\n[u-s*sin(u),1-s*cos( u),s=0..1]\},\nu=0..4*Pi, color=red):\ndisplay(a1,insequence=true):" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 113 "Next we create an animation of \+ the cycloid curve, and save it in a variable named `a2 ' but we don't display it." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "a2 := animate([x(u* t),y(u*t),t=0..4*Pi],\nu=0..1,color=blue):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 118 "And now, we display both animations together so you can see the point on the end of the spoke generating the cycloid." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "display(\{a1, a2\});" }}{PARA 13 " " 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%(ANIMATEG627%-%'CURVESG6 $7S7$\"\"!F,7$$!1;0?A>E08!#;$\"1='*=E'Q^b)!#=7$$!12_-^/>)e#F0$\"1pJ4rt T2M!#<7$$!1)*3lBV$o#QF0$\"1E8()[n/7wF97$$!1**************\\F0$\"18c:if 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