{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 2 
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2 1 2 0 0 0 1 }{CSTYLE "_cstyle2" -1 202 "Courier" 0 1 255 0 0 1 0 1 
0 2 1 2 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 
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Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 
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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 8 "restart:" }}}
{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 12 "with(plots):" }}}{EXCHG 
{PARA 200 "> " 0 "" {MPLTEXT 1 202 62 "CatLists:=proc(L1,L2)\n [op(L1)
,seq(L2[-i],i=1..nops(L2))]\nend:" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 201 9 "theta:=0:" }{MPLTEXT 1 202 10 "\nalpha:=1:" }}{PARA 
200 "> " 0 "" {MPLTEXT 1 201 118 "u:=proc(t)\n global theta,alpha:\n i
f (t<abs(theta)) then\n  alpha*signum(theta)\n else \n  -alpha*signum(
theta) \n fi:\nend:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 47 "
F:=proc(N,t,x,f)\n f[1]:=x[2];\n f[2]:=u(t):\nend:" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 201 132 "sol:=dsolve(numeric,number=2,procedu
re=F,start=0,initial=array([0,0]),\n procvars=[x1(t),x2(t)],startinit=
true,output=listprocedure);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 
201 12 "assign(sol);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 21 
"x1:=x1(t);\nx2:=x2(t);" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 " \317
\360\356\366\345\344\363\360\340 X1" }}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 201 56 "X1:=proc(t,tau)\n global theta:\n theta:=tau:\n x1(
t);\nend:" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 " \317\360\356\366
\345\344\363\360\340 X2" }}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 
56 "X2:=proc(t,tau)\n global theta:\n theta:=tau:\n x2(t);\nend:" }}}}
{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 5 "T:=5;" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 202 18 "eps:=Float(1,-16);" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 201 121 "d1:=plot(['X1'(T,tau),'X2'(T,tau),ta
u=0+eps..T],color=blue):\nd2:=plot(['X1'(T,tau),'X2'(T,tau),tau=-T..0-
eps],color=red):" }{MPLTEXT 1 202 96 "\ngT:=textplot([-10,4,cat(`T = `
,convert(T,string))],align=\{ABOVE,RIGHT\},font=[COURIER,BOLD,16]):" }
}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 37 "display(d1,d2,gT,label
s=['x1','x2']);" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 6 "N:=50
;" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 201 44 "G:=NULL:\nold:=tim
e():\nfor i from 0 to N do\n " }{MPLTEXT 1 202 13 "M:=iquo(i,5);" }
{MPLTEXT 1 201 84 "\n t:=evalf(i*T/N,4);\n if(irem(i,5) = 0) then\n  p
rint(cat(`t = `,convert(t,string)));" }{MPLTEXT 1 202 40 "\n  print(ca
t(`M = `,convert(M,string)));" }{MPLTEXT 1 201 130 "\n fi;\n d1:=plot(
['X1'(t,tau),'X2'(t,tau),tau=0+eps..t-eps]):\n d2:=plot(['X1'(t,tau),'
X2'(t,tau),tau=-t+eps..0-eps]):\n ts:=sprintf(" }{MPLTEXT 1 202 7 "\"%
3.1f\"" }{MPLTEXT 1 201 10 ",t):\n d3:=" }{MPLTEXT 1 202 90 "textplot(
[-12,4,cat(`T = `,convert(ts,string))],align=\{ABOVE,RIGHT\},font=[TIM
ES,BOLD,16]):" }{MPLTEXT 1 201 6 "\n d4:=" }{MPLTEXT 1 202 134 "POLYGO
NS(CatLists(op([1,1],d1),op([1,1],d2)),\n  COLOR(RGB,226/256,226/256,2
26/256),STYLE(PATCHNOGRID)):\n InPs:=NULL:\n alphaold:=alpha:" }
{MPLTEXT 1 201 182 "\n for j from 1 to M-1 do\n  alpha:=j*alphaold/M;
\n  plot(['X1'(t,tau),'X2'(t,tau),tau=-t..0-eps],numpoints=i);\n  plot
(['X1'(t,tau),'X2'(t,tau),tau=0+eps..T],numpoints=i);\n  InPs:=InPs," 
}{MPLTEXT 1 202 125 "\n   POINTS(op(op([1,1],%%)),COLOR(RGB,0,0,1),SYM
BOL(CIRCLE,4)),\n   POINTS(op(op([1,1],%)) ,COLOR(RGB,1,0,0),SYMBOL(CI
RCLE,4))" }{MPLTEXT 1 201 148 "; \n od:\n alpha:=alphaold:\n G:=G,PLOT
(\n  InPs,\n  CURVES(op([1,1],d1),COLOR(RGB,1,0,0)),\n  CURVES(op([1,1
],d2),COLOR(RGB,0,0,1)),\n  op(d3),\n  d4):\nod:" }{MPLTEXT 1 202 50 "
\nprint(cat(`Time = `,convert(time()-old,string)));" }}}{EXCHG {PARA 
200 "> " 0 "" {MPLTEXT 1 201 105 "display([G],insequence=true,title=\"
Attainability Domain\",titlefont=[TIMES,BOLD,16],\n labels=['x1','x2']
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19" 0 }{VIEWOPTS 1 1 1 1 1 1803 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }