{VERSION 5 0 "IBM INTEL NT" "5.0" }
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 20 "restart
;with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "s1:=(x,y) ->
sqrt((x+r1)^2+y^2):\ns2:=(x,y) ->sqrt((x-r2)^2+y^2):\nveff:=(x,y) -> -
((x^2+y^2)/2+r2/s1(x,y)+r1/s2(x,y)):\nfx:=-diff(veff(x,y),x)+2*vy:\nfy
:=-diff(veff(x,y),y)-2*vx:" "6#C'>%#s1Gf*6$%\"xG%\"yG7\"6$%)operatorG%
&arrowG6\"-%%sqrtG6#,&*$,&F(\"\"\"%#r1GF5\"\"#F5*$F)F7F5F.F.F.>%#s2Gf*
6$F(F)7\"6$F,F-F.-F06#,&*$,&F(F5%#r2G!\"\"F7F5*$F)F7F5F.F.F.>%%veffGf*
6$F(F)7\"6$F,F-F.,$,(*&,&*$F(F7F5*$F)F7F5F5F7FEF5*&FDF5-F%6$F(F)FEF5*&
F6F5-F:6$F(F)FEF5FEF.F.F.>%#fxG,&-%%diffG6$-FH6$F(F)F(FE*&F7F5%#vyGF5F
5>%#fyG,&-Fgn6$-FH6$F(F)F)FE*&F7F5%#vxGF5FE" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 40 "subf:=\{x=x(t),y=y(t),vx=vx(t),vy=vy(t)\}:" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "eqs:=diff(x(t),t)=vx(t),\n    \+
  diff(y(t),t)=vy(t),\n      diff(vx(t),t)=subs(subf,fx),\n      diff(
vy(t),t)=subs(subf,fy):" "6#>%$eqsG6&/-%%diffG6$-%\"xG6#%\"tGF--%#vxG6
#F-/-F(6$-%\"yG6#F-F--%#vyG6#F-/-F(6$-F/6#F-F--%%subsG6$%%subfG%#fxG/-
F(6$-F86#F-F--F@6$FB%#fyG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
298 "LagrPnts:=proc(a)\nlocal l1,l2,l3,l4:\nglobal x1,x2,x3,x4,y4,r1,r
2:\nr2:=1/(1+a):r1:=1-r2:\nl1:=(r2/(x+r1)^2+r1/(x-r2)^2)-x:x1:=fsolve(
l1,x=r2..2):\nl2:=(r2/(x+r1)^2-r1/(x-r2)^2)-x:x2:=fsolve(l2,x=0..r2):
\nl3:=(r2/(x+r1)^2+r1/(x-r2)^2)+x:x3:=fsolve(l3,x=-2..-r1):\nx4:=(r2-r
1)/2:y4:=evalf(sqrt(3)/2):\nend:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "LagrPnts(0.18):print(r1,r2,x1,x2,x3,x4,y4);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }{MPLTEXT 1 
0 10 "veff(x,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 185 "pl:=pl
ot3d(\{[x1,0,veff(x1,0)],[x2,0,veff(x2,0)],[x3,0,veff(x3,0)],[x4,y4,ve
ff(x4,y4)],[x4,-y4,veff(x4,-y4)]\},x=-1.5..1.5,y=-1.4..1.4,style=point
,symbol=cross,color=black,symbolsize=30):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 257 "Vmin:=-4:nc:=20:\ncons := [ seq(k/nc*Vmin, k=0..nc-1
) ]: \npv:=plot3d([x,y,veff(x,y)], \n        x=-1.5..1.5, y=-1.4..1.5,
grid=[40,40],contours=cons,view=Vmin..-1,\nlabels=[`x`,`y`,`Veff`],lig
htmodel=light1,axes=FRAMED,style=PATCHCONTOUR,orientation=[-23,53]):\n
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "display(\{pl,pv\});" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 308 "a := .953875e-3:LagrPnts(a):print(
r1,r2,x1,x2,x3,x4,y4);\nLPnts:=[[x1,0]],[[x2,0]],[[x3,0]],[[x4,y4]],[[
x4,-y4]]:\nppl:=plot([LPnts],style=point,symbol=diamond,symbolsize=15,
colour=blue):\nbodies:=[-r1,0],[r2,0]:\nppb:=plot([bodies],style=point
,\n          symbol=[circle,circle],symbolsize=[30,10],colour=brown):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "funs:=\{x(t),y(t),vx(t)
,vy(t)\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "ini0:=x(0)=x4
*1.01,y(0)=y4*1.01,vx(0)=0.01,vy(0)=0.01:\nran:=0..200:\ndsol0:=dsolve
([eqs,ini0],numeric,funs,range=ran):\npl:=odeplot(dsol0,[x(t),y(t)],ra
n,labels=[x,y],\nview=[-2..2, -2..2]):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "display(\{pl,ppl,ppb\});" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{MARK "13" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }