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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 
"" {TEXT 256 12 "EARTH HOCKEY" }}{PARA 258 "" 0 "" {TEXT 259 11 "Tevia
n Dray" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 257 
34 "copyright 1998-2000 by Tevian Dray" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 259 "" 0 "" {TEXT 258 41 "Which way does the hockey puck rea
lly go?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "read(`/usersB/tevian/maple/ph429/EarthHockey`):" }}}
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{TEXT -1 5 "Demos" }}{PARA 0 "" 0 "" {TEXT -1 78 "Imagine the Earth as
 a smooth hockey rink.  What happens when the puck is hit?" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 105 "First, we set so
me parameters.  The angular velocity of the Earth (in radians/second) \+
will be denoted by " }{XPPEDIT 18 0 "Omega" "6#%&OmegaG" }{TEXT -1 2 "
; " }{XPPEDIT 18 0 "Omega" "6#%&OmegaG" }{TEXT -1 17 " is positive for
 " }{TEXT 261 16 "counterclockwise" }{TEXT -1 143 " rotation as seen l
ooking down at the North Pole from above, corresponding to west-to-eas
t rotation.  The total number of pictures is given by " }{XPPEDIT 18 
0 "N" "6#%\"NG" }{TEXT -1 23 "; a reasonable value is" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "N:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"NG\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 55 "(A smoother animation is o
btained for larger values of " }{XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 
2 "; " }{XPPEDIT 18 0 "N=10" "6#/%\"NG\"#5" }{TEXT -1 41 " works fairl
y well.  But large values of " }{XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 
74 " may also take significantly longer to run.  See what works well f
or you.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
60 "Choose how you want the graphics to be displayed, using any " }
{TEXT 260 3 "one" }{TEXT -1 18 " of the following:" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "plotsetup(inline):" }{TEXT -1 26 "     (grap
hs in worksheet)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plotset
up(window):" }{TEXT -1 29 "     (graphs in Maple window)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "plotsetup(x11):" }{TEXT -1 41 "    \+
        (graphs in separate X window)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 386 "In the figures you will construct, the blue arrow repres
ents the motion of the puck as seen by an inertial observer, while the
 red curve represents the motion as seen by the rotating observer.  (T
he green curve is to help you keep track of the rotation.)  Think of t
he tip of the blue curve as containing red dye which writes on the Ear
th as the Earth rotates beneath the (moving) puck." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "The demo shows what the n
onrotating observer sees, and takes the form" }}{PARA 260 "" 0 "" 
{TEXT -1 1 " " }{XPPEDIT 18 0 "Geod(latitude,angle,N,Omega" "6#-%%Geod
G6&%)latitudeG%&angleG%\"NG%&OmegaG" }{TEXT -1 1 " " }}{PARA 0 "" 0 "
" {TEXT -1 6 "Here, " }{XPPEDIT 18 0 "N" "6#%\"NG" }{TEXT -1 2 ", " }
{XPPEDIT 18 0 "Omega" "6#%&OmegaG" }{TEXT -1 23 " are as defined above
, " }{XPPEDIT 18 0 "latitude" "6#%)latitudeG" }{TEXT -1 42 " denotes t
he initial (Northern) latitude, " }{XPPEDIT 18 0 "angle" "6#%&angleG" 
}{TEXT -1 68 " denotes the initial angle of motion (both in radians) a
s seen by a " }{TEXT 262 11 "nonrotating" }{TEXT -1 10 " observer." }}
{PARA 0 "" 0 "" {TEXT -1 62 "You can also specify the initial angle of
 motion as seen by a " }{TEXT 263 8 "rotating" }{TEXT -1 15 " observer
 using" }}{PARA 262 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "RGeod(latit
ude,Rangle,N,Omega" "6#-%&RGeodG6&%)latitudeG%'RangleG%\"NG%&OmegaG" }
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 32 "which simply converts th
e angle " }{TEXT 264 6 "Rangle" }{TEXT -1 54 " from the rotating to th
e nonrotating frame and calls " }{TEXT -1 5 "Geod." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 274 "Please note that the mot
ion is actually shown starting and ending at the Equator,  but passing
 through the given latitude at the given angle.  Furthermore, rather t
han changing the velocity of the puck, it turns out to be easier (to p
rogram!) to change the angular velocity " }{XPPEDIT 18 0 "Omega" "6#%&
OmegaG" }{TEXT -1 241 " of the Earth.  In particular, while you can't \+
get the puck to go in the other direction, you can turn the Earth arou
nd!  (You can, of course, change the point of view after creating the \+
animation.  If you are unsure how to do this, see me.)" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "For example, try" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Geod(Pi/4,Pi,N,1.5);" }}}
{EXCHG {PARA 261 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "Geod(0,15*Pi/32,N,3);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "RGeod(Pi/4,
Pi/2,N,.5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 21 "Geod(Pi/4,Pi/2,N,.5);" }}}{EXCHG {PARA 0 
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