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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 99 "This Maple Worksheet produces the solution to the rocket launch
 linear program, with air resistance" }}{PARA 0 "" 0 "" {TEXT -1 28 "a
nd a soft landing (v(T)=0)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "with(simplex):" }}{PARA 7 "" 1 "" {TEXT -1 
87 "Warning, the protected names maximize and minimize have been redef
ined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 117 "Define the parameters N (number of inter
vals), T (total time), g (gravity), a0=maximum acceleration, h=desired
 height" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "N:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"\"&" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "T:=20;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"TG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
6 "g:=32;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG\"#K" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a0:=80;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#a0G\"#!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
7 "h:=400;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG\"$+%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "tau:=T/N;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$tauG\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 34 "Extra constant for air resistance:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "k:=0.4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG$\"\"%!\"\"" }}}
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "We
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-1 47 "Soft landing gives an extra constraint (v(T)=0)" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "CS6:=s
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{XPPMATH 20 "6#>%\"ZG<,/&%\"xG6#\"\"$$\"+tZkp]!\")/&F(6#\"\"%$!++++lR!
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{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 94 "Now that we have the opti
mal values, construct the position, velocity and acceleration values:
" }}{PARA 0 "" 0 "" {TEXT -1 40 "  First, the desired values will be i
n A" }}{PARA 0 "" 0 "" {TEXT -1 83 "  Next, get the sequence of veloci
ties and positions (See Equations  3.17 and 3.18)" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "assign(Z); \+
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96 "For the acceleration, velocity and position functions, we'll use H
eaviside functions rather than" }}{PARA 0 "" 0 "" {TEXT -1 70 "piecewi
se defined functions...  Just a matter of taste, not substance." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
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