{VERSION 2 3 "IBM INTEL NT" "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 "" 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 54 "ellips0.mws numerical integration of elliptical o rbit" }}{PARA 0 "" 0 "" {TEXT -1 52 "revised ellips0 with better plot \+ of energy 10/14/98" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart;with(plots):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 11 "Digits:=12;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "mu:=0.4; # mass = Msun/100. (Danby's mu = GM)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "x0:=1; xdot0:=0;y0:=0;ydot0: =4/10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "r0:=sqrt(x0^2+y0^ 2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Energy0:=1/2*(xdot0^ 2+ydot0^2)-mu/r0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "rm3:=m u/(x(t)^2+y(t)^2)^(3/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eq1:=diff(x(t),t,t) = -x(t)*rm3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "eq2:=diff(y(t),t,t) = -y(t)*rm3;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 85 "s:=dsolve(\{eq1,eq2,x(0)=x0,D(x)(0)=xdot0,y( 0)=y0,D(y)(0)=ydot0\},[x(t),y(t)],numeric);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "xp:= z -> rhs(s(z)[2]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "yp:= z -> rhs(s(z)[4]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot([xp,yp,0..7],numpo ints=200);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ke:= z -> (rh s(s(z)[3])^2+rhs(s(z)[5])^2)/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "pe:= z -> -0.4/(rhs(s(z)[2])^2+rhs(s(z)[4])^2)^(1/2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([ke+pe,z],0..7); # ener gy plot - should be constant" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "plot(ke+pe,0..7); # better way to do the same plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 1 0" 52 }{VIEWOPTS 1 1 0 1 1 1803 }