{VERSION 5 0 "APPLE_PPC_MAC" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 
"" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 14 0 0 0 
0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 8 0 0 0 0 1 0 0 0 0 0 0 
0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "
" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 
1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 
0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 
259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "
" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 
0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE 
"" 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 
-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 0 1 
0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 
"" {TEXT 256 23 "CONSTRUCTING SOLUTIONS\n" }{TEXT 257 13 "Tevian Dray
\n\n" }{TEXT 258 32 "copyright 1998-2000 Tevian Dray\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 42 "Choose arbitrary linear functions for the " }{XPPEDIT 18 
0 "x" "6#%\"xG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "y" "6#%\"yG" }
{TEXT -1 69 " coordinates of the pen.  In other words, choose arbitrar
y values of " }{XPPEDIT 18 0 "x[0]" "6#&%\"xG6#\"\"!" }{TEXT -1 2 ", \+
" }{XPPEDIT 18 0 "y[0]" "6#&%\"yG6#\"\"!" }{TEXT -1 2 ", " }{XPPEDIT 
18 0 "v[x]" "6#&%\"vG6#%\"xG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "v[y]" "
6#&%\"vG6#%\"yG" }{TEXT -1 20 ", in the expressions" }}{PARA 257 "" 0 
"" {TEXT -1 1 " " }{XPPEDIT 18 0 "x=x[0]+v[x]*t" "6#/%\"xG,&&F$6#\"\"!
\"\"\"*&&%\"vG6#F$F)%\"tGF)F)" }{TEXT -1 1 " " }}{PARA 258 "" 0 "" 
{TEXT -1 1 " " }{XPPEDIT 18 0 "y=y[0]+v[y]*t" "6#/%\"yG,&&F$6#\"\"!\"
\"\"*&&%\"vG6#F$F)%\"tGF)F)" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 
-1 93 "and enter the resulting formulas below.  (Don't forget to end e
ach command with a semicolon!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 3 "x:=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "y:=" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Now choose an angular velocity " }
{XPPEDIT 18 0 "Omega;" "6#%&OmegaG" }{TEXT -1 10 ", so that " }
{XPPEDIT 18 0 "theta = Omega*t;" "6#/%&thetaG*&%&OmegaG\"\"\"%\"tGF'" 
}{TEXT -1 1 "." }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 56 "You may find \+
it helpful to first record your values of  " }{XPPEDIT 18 0 "Omega;" "
6#%&OmegaG" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }
{TEXT -1 6 " here:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Omega:
=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "theta:=" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 39 "Now transform to rotating coordinates (" 
}{XPPEDIT 18 0 "X,Y;" "6$%\"XG%\"YG" }{TEXT -1 38 ") using the formula
s derived in class:" }}{PARA 259 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 
0 "X=x*cos(theta)+y*sin(theta)-R" "6#/%\"XG,(*&%\"xG\"\"\"-%$cosG6#%&t
hetaGF(F(*&%\"yGF(-%$sinG6#F,F(F(%\"RG!\"\"" }{TEXT -1 1 " " }}{PARA 
260 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "Y=-x*sin(theta)+y*cos(theta
)" "6#/%\"YG,&*&%\"xG\"\"\"-%$sinG6#%&thetaGF(!\"\"*&%\"yGF(-%$cosG6#F
,F(F(" }{TEXT -1 1 " " }}{PARA 263 "" 0 "" {TEXT -1 32 "(It is safe to
 assume here that " }{XPPEDIT 18 0 "R=0" "6#/%\"RG\"\"!" }{TEXT -1 46 
", i.e. that both frames have the same origin.)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 3 "X:=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
3 "Y:=" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Verify that these expre
ssions solve the differential equations derived in class:" }}{PARA 
261 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "diff(X,t,t)-2*Omega*diff(Y,
t)-Omega^2*(X+R)=0" "6#/,(-%%diffG6%%\"XG%\"tGF)\"\"\"*(\"\"#F*%&Omega
GF*-F&6$%\"YGF)F*!\"\"*&F-F,,&F(F*%\"RGF*F*F1\"\"!" }{TEXT -1 1 " " }}
{PARA 262 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "diff(Y,t,t)+2*Omega*d
iff(X,t)-Omega^2*Y=0" "6#/,(-%%diffG6%%\"YG%\"tGF)\"\"\"*(\"\"#F*%&Ome
gaGF*-F&6$%\"XGF)F*F**&F-F,F(F*!\"\"\"\"!" }{TEXT -1 1 " " }}{PARA 0 "
" 0 "" {TEXT -1 1 "(" }{TEXT 260 43 "Second derivatives can be entered
 as either" }{TEXT -1 1 " " }{MPLTEXT 0 21 13 " diff(X,t,t) " }{TEXT 
259 2 "or" }{TEXT -1 3 "   " }{MPLTEXT 0 21 12 "diff(X,t$2) " }{TEXT 
-1 2 ")." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }