{VERSION 4 0 "IBM INTEL NT" "4.0" }
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0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "Here are some computation
s that are relevant for Keplers Laws.  It's amazing how things eventua
lly get simple!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart;
with(linalg):\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected
 names norm and trace have been redefined and unprotected\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "x(t):=r(t)*cos(theta(t));y(t
):=r(t)*sin(theta(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"xG6#%\"
tG*&-%\"rGF&\"\"\"-%$cosG6#-%&thetaGF&F+" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%\"yG6#%\"tG*&-%\"rGF&\"\"\"-%$sinG6#-%&thetaGF&F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "vx:=diff(x(t),t);vy:=diff(y(t),t);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vxG,&*&-%%diffG6$-%\"rG6#%\"tGF
-\"\"\"-%$cosG6#-%&thetaGF,F.F.*(F*F.-%$sinGF1F.-F(6$F2F-F.!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vyG,&*&-%%diffG6$-%\"rG6#%\"tGF-\"
\"\"-%$sinG6#-%&thetaGF,F.F.*(F*F.-%$cosGF1F.-F(6$F2F-F.F." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ax:=diff(vx,t);ay:=diff(vy,t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#axG,**&-%%diffG6$-%\"rG6#%\"tG-%\"$
G6$F-\"\"#\"\"\"-%$cosG6#-%&thetaGF,F2F2**F1F2-F(6$F*F-F2-%$sinGF5F2-F
(6$F6F-F2!\"\"*(F*F2F3F2)F=F1F2F?*(F*F2F;F2-F(6$F6F.F2F?" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#ayG,**&-%%diffG6$-%\"rG6#%\"tG-%\"$G6$F-\"\"#
\"\"\"-%$sinG6#-%&thetaGF,F2F2**F1F2-F(6$F*F-F2-%$cosGF5F2-F(6$F6F-F2F
2*(F*F2F3F2)F=F1F2!\"\"*(F*F2F;F2-F(6$F6F.F2F2" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 83 "radial_compent_of_acc:=dotprod([ax,ay],[cos(th
eta(t)),sin(theta(t))],'orthogonal');" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>%6radial_compent_of_accG,&*&,**&-%%diffG6$-%\"rG6#%\"tG-%\"$G6$F/
\"\"#\"\"\"-%$cosG6#-%&thetaGF.F4F4**F3F4-F*6$F,F/F4-%$sinGF7F4-F*6$F8
F/F4!\"\"*(F,F4F5F4)F?F3F4FA*(F,F4F=F4-F*6$F8F0F4FAF4F5F4F4*&,**&F)F4F
=F4F4**F3F4F;F4F5F4F?F4F4*(F,F4F=F4FCF4FA*(F,F4F5F4FEF4F4F4F=F4F4" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "theta_component_of_acc:=dotp
rod([ax,ay],[-sin(theta(t)),cos(theta(t))],'orthogonal');" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#>%7theta_component_of_accG,&*&,**&-%%diffG6$-%
\"rG6#%\"tG-%\"$G6$F/\"\"#\"\"\"-%$cosG6#-%&thetaGF.F4F4**F3F4-F*6$F,F
/F4-%$sinGF7F4-F*6$F8F/F4!\"\"*(F,F4F5F4)F?F3F4FA*(F,F4F=F4-F*6$F8F0F4
FAF4F=F4FA*&,**&F)F4F=F4F4**F3F4F;F4F5F4F?F4F4*(F,F4F=F4FCF4FA*(F,F4F5
F4FEF4F4F4F5F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "rad_com
p_acc:=simplify(radial_compent_of_acc,\{sin(theta(t))^2+cos(theta(t))^
2=1\});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "theta_comp_acc:=simplify
(theta_component_of_acc,\{sin(theta(t))^2+cos(theta(t))^2=1\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-rad_comp_accG,&-%%diffG6$-%\"rG6#%
\"tG-%\"$G6$F,\"\"#\"\"\"*&F)F1)-F'6$-%&thetaGF+F,F0F1!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%/theta_comp_accG,&*&-%%diffG6$-%\"rG6#%\"t
GF-\"\"\"-F(6$-%&thetaGF,F-F.\"\"#*&F*F.-F(6$F1-%\"$G6$F-F3F.F." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "dA:=r(t)^2*diff(theta(t),t);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dAG*&)-%\"rG6#%\"tG\"\"#\"\"\"-
%%diffG6$-%&thetaGF)F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 
"factor(diff(dA,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%\"rG6#%\"t
G\"\"\",&*&-%%diffG6$F$F'F(-F,6$-%&thetaGF&F'F(\"\"#*&F$F(-F,6$F0-%\"$
G6$F'F2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "r(t)*theta
_comp_acc-factor(diff(dA,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "11 0 0" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }