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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Global Stability Worked Ex
ample 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
110 " To examine the long term behaviour of the simple pendulum modell
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69 "The equation can therefore be represented by the the nonlinear sys
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-1 44 "To prove the system is reversible substitute" }}{PARA 0 "" 0 "
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0 "" {TEXT -1 29 "into the system of equations." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "F:=diff(x(t),t)=y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"FG/-%%diffG6$-%\"xG6#%\"tGF,%\"yG" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "G:=diff(y(t),t)=(g/l)*sin(x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"GG/-%%diffG6$-%\"yG6#%\"tGF,*(%\"gG\"\"
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0 81 "subs(\{t=-t,y=-y,diff(x(t),t)=-diff(x(t),t),x=x,diff(y(t),t)=dif
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-%\"yG6#%\"tGF+*(%\"gG\"\"\"%\"lG!\"\"-%$sinG6#%\"xGF./,$-F&6$-F4F*F+F
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{PARA 0 "" 0 "" {TEXT -1 103 "These two equations are identical to the
 original two equations and therefore the system is reversible." }}}}
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