{VERSION 2 3 "SGI IRIS UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "New century schoo lbook" 1 18 0 0 0 0 1 1 2 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 }1 0 0 0 6 6 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 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica " 1 18 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 3 " -1 258 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 4" -1 259 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 5" -1 260 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 6" -1 261 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 7" -1 262 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 0 0 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 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 }{PSTYLE "" 0 265 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 {PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 22 "Calulus Worksheet VI\n\n" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 101 " In this worksheet we give a few examples how Maple can be used for ani mation. Load the plots package:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 31 "Animate a simple function plot:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 " animate(sin(x*t), x=-10..10,t=1..2,\nthickness=3, color=red, numpoints =100, frames=20);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 25 "Animate pa rametric plots:" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 46 "Animate a roll ing circle as a parametric plot:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "animate([t+cos(u),sin(u),u=0..2*Pi], t=0..2*Pi,\naxes=none, c olor=red, thickness=3, scaling=constrained, frames=20);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "With background plot:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 167 "display( \{\nanimate([t+cos(u),1+sin(u),u=0 ..2*Pi], t=0..2*Pi,\ncolor=red, thickness=3, frames=20),\nplot(0, x=-1 ..2*Pi+1, color=blue) \n\}, scaling=constrained, axes=none);" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Combined animations:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 197 "animate(\{ \n[cos(t)+0.05*cos(u),s in(t)+0.05*sin(u), u=0..2*Pi,color=red],\n[(u-0.05)*cos(t),(u-0.05)*si n(t),u=0..1] \n\}, \nt=0..2*Pi,\naxes=none, color=red, thickness=3, sc aling=constrained, frames=20);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "Rotating segment:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "an imate([cos(t)*u,sin(t)*u,u=-2..2], t=0..2*Pi,\ncolor=aquamarine, axes= none, thickness=3, scaling=constrained, frames=20);" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 28 "Drawing curves by animation:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "animate([cos(t*u),sin(t*u),u=0..1] , t=0..2*Pi,\naxes=none, color=red, thickness=3, scaling=constrained, \+ frames=20);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "display( \{ \nanimate(\n[cos(t)*u,sin(t)*u,u=0..1], t=0..2*Pi,\ncolor=magenta),\na nimate(\n[cos(t*u),sin(t*u),u=0..1], t=0..2*Pi,\ncolor=blue)\n\}, \nth ickness=3, axes=none, scaling=constrained);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Animate the the cycloid:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "circle := animate(\n[t+cos(u),1+sin(u),u=0..2*Pi], t= 0..3*Pi,\ncolor=cyan, frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "base := plot(0, x=-1..3*Pi+1, color=blue):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "display(\{circle, base\},\nt hickness=3, axes=none, scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "P:=(t,l)->[t-l*sin(t),1-l*cos(t)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "cyc := l->animate(\n\{ [u*P(t,l)[1 ]+(1-u)*P(t,0)[1], u*P(t,l)[2]+(1-u)*P(t,0)[2], u=0..1],\n [P(t*u,l) [1], P(t*u,l)[2], u=0..1] \}, t=0..3*Pi,\ncolor=red, frames=20):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "display(\{circle, base, cyc( 1)\},\nthickness=3, axes=none, scaling=constrained);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 27 "Animate the the epicycloid:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "rolloncircle := r->animate( [(1+r) *cos(t)+r*cos(u),(1+r)*sin(t)+r*sin(u),\nu=0..3*Pi], \nt=0..2*Pi,\ncol or=cyan, frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "bas ecircle:= plot([cos(u),sin(u),u=0..2*Pi], color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "display(\{ basecircle, rolloncircle (1/2)\},\nthickness=3, axes=none, scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Q:=(t,r,l)->\n[(1+r)*cos(t)-l*cos(( 1+1/r)*t),\n(1+r)*sin(t)-l*sin((1+1/r)*t)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "epicycle := (r,l)->animate( \{ [u*Q(t,r,l)[1]+(1- u)*Q(t,r,0)[1],\nu*Q(t,r,l)[2]+(1-u)*Q(t,r,0)[2],u=0..1],\n[Q(t*u,r,l) [1],Q(t*u,r,l)[2],u=0..1] \n\}, t=0..2*Pi,\nnumpoints=200, color=red, \+ frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "display(\{b asecircle, rolloncircle(1/2),epicycle(1/2,3/2)\},\nthickness=3, axes=n one, scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "display(\{basecircle,\nrolloncircle(1/4),epicycle(1/4,2)\},\ninse quence=false, thickness=3, axes=none, scaling=constrained);" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 28 "Animate the the hypocycloid:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "rollincircle := r->animate( \n[(1-r)*cos(t)+r*cos(u),(1-r)*sin(t)+r*sin(u),\nu=0..3*Pi],\nt=0..2*P i,\ncolor=cyan, frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "display(basecircle, \nrollincircle(1/2),\nthickness=3, axes=none, \+ scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "R: =(t,r,l)->[(1-r)*cos(t)+l*cos((1-1/r)*t),\n(1-r)*sin(t)+l*sin((1-1/r)* t)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "hypocycle := (r,l) ->animate(\n\{ [u*R(t,r,l)[1]+(1-u)*R(t,r,0)[1],\nu*R(t,r,l)[2]+(1-u)* R(t,r,0)[2],u=0..1],\n[R(t*u,r,l)[1],R(t*u,r,l)[2],u=0..1] \}, \nt=0.. 2*Pi,\nnumpoints=200, color=red, frames=20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "display(\{basecircle,\nrollincircle(1/4),hypocy cle(1/4,1/4)\},\ninsequence=false, thickness=3, axes=none, scaling=con strained,\ntitle=`The Astroid Animated`);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 105 "display(\{basecircle,\nrollincircle(1/3),hypocycle (1/3,2/3)\},\nthickness=3, axes=none, scaling=constrained);" }}}}} {MARK "4 2" 0 }{VIEWOPTS 1 1 0 3 2 1804 }