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{SECT 0 {EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 21 "restart;with(lin
alg):" }}{PARA 201 "" 1 "" {TEXT 203 79 "Warning, the protected names \+
norm and trace have been redefined and unprotected" }{TEXT 203 0 "" }}
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 80 "ur:=vector([sin(theta(t
))*cos(phi(t)),sin(theta(t))*sin(phi(t)),cos(theta(t))]);" }{MPLTEXT 
1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I#urG6\"-I'vectorG6$I*p
rotectedGF)I(_syslibGF%6#7%*&-I$sinGF(6#-I&thetaGF%6#I\"tGF%\"\"\"-I$c
osGF(6#-I$phiGF%F3F5*&F.F5-F/F8F5-F7F0" }{TEXT 204 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {MPLTEXT 1 202 85 "utheta:=vector([cos(theta(t))*c
os(phi(t)),cos(theta(t))*sin(phi(t)),-sin(theta(t))]);" }{MPLTEXT 1 
202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I'uthetaG6\"-I'vectorG6$I
*protectedGF)I(_syslibGF%6#7%*&-I$cosGF(6#-I&thetaGF%6#I\"tGF%\"\"\"-F
/6#-I$phiGF%F3F5*&F.F5-I$sinGF(F7F5,$-F<F0!\"\"" }{TEXT 204 0 "" }}}
{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 43 "uphi:=vector([-sin(phi(t
)),cos(phi(t)),0]);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#>I%uphiG6\"-I'vectorG6$I*protectedGF)I(_syslibGF%6#7%,$
-I$sinGF(6#-I$phiGF%6#I\"tGF%!\"\"-I$cosGF(F0\"\"!" }{TEXT 204 0 "" }}
}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 24 "OM:=map(u->u*rho(t),ur)
;" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I#OMG6\"-I
'vectorG6$I*protectedGF)I(_syslibGF%6#7%*(-I$sinGF(6#-I&thetaGF%6#I\"t
GF%\"\"\"-I$cosGF(6#-I$phiGF%F3F5-I$rhoGF%F3F5*(F.F5-F/F8F5F;F5*&-F7F0
F5F;F5" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 
22 "deriver:=u->diff(u,t);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#>I(deriverG6\"f*6#I\"uGF%F%6$I)operatorGF%I&arrowGF%F%-
I%diffGI*protectedGF.6$9$I\"tGF%F%F%F%" }{TEXT 204 0 "" }}}{EXCHG 
{PARA 200 "> " 0 "" {MPLTEXT 1 202 19 "v:=map(deriver,OM);" }{MPLTEXT 
1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"vG6\"-I'vectorG6$I*p
rotectedGF)I(_syslibGF%6#7%,(**-I$cosGF(6#-I&thetaGF%6#I\"tGF%\"\"\"-I
%diffGF)6$F2F5F6-F06#-I$phiGF%F4F6-I$rhoGF%F4F6F6**-I$sinGF(F1F6-FBF;F
6-F86$F<F5F6F>F6!\"\"*(FAF6F:F6-F86$F>F5F6F6,(**F/F6F7F6FCF6F>F6F6**FA
F6F:F6FDF6F>F6F6*(FAF6FCF6FHF6F6,&*(FAF6F7F6F>F6FF*&F/F6FHF6F6" }
{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 18 "a:=map
(deriver,v);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#
>I\"aG6\"-I'vectorG6$I*protectedGF)I(_syslibGF%6#7%,2**-I$sinGF(6#-I&t
hetaGF%6#I\"tGF%\"\"\"-I%diffGF)6$F2F5\"\"#-I$cosGF(6#-I$phiGF%F4F6-I$
rhoGF%F4F6!\"\"**-F<F1F6-F86$F2-I\"$GF)6$F5F:F6F;F6F@F6F6*,FDF6F7F6-F0
F=F6-F86$F>F5F6F@F6!\"#**FDF6F7F6F;F6-F86$F@F5F6F:**F/F6F;F6FLF:F@F6FB
**F/F6FKF6-F86$F>FGF6F@F6FB**F/F6FKF6FLF6FPF6FN*(F/F6F;F6-F86$F@FGF6F6
,2**F/F6F7F:FKF6F@F6FB**FDF6FEF6FKF6F@F6F6*,FDF6F7F6F;F6FLF6F@F6F:**FD
F6F7F6FKF6FPF6F:**F/F6FKF6FLF:F@F6FB**F/F6F;F6FTF6F@F6F6**F/F6F;F6FLF6
FPF6F:*(F/F6FKF6FXF6F6,**(FDF6F7F:F@F6FB*(F/F6FEF6F@F6FB*(F/F6F7F6FPF6
FN*&FDF6FXF6F6" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" 
{MPLTEXT 1 202 100 "V:=vector([dotprod(v,ur,'orthogonal'),dotprod(v,ut
heta,'orthogonal'),dotprod(v,uphi,'orthogonal')]);" }{MPLTEXT 1 202 0 
"" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"VG6\"-I'vectorG6$I*protected
GF)I(_syslibGF%6#7%,(*(,(**-I$cosGF(6#-I&thetaGF%6#I\"tGF%\"\"\"-I%dif
fGF)6$F4F7F8-F26#-I$phiGF%F6F8-I$rhoGF%F6F8F8**-I$sinGF(F3F8-FDF=F8-F:
6$F>F7F8F@F8!\"\"*(FCF8F<F8-F:6$F@F7F8F8F8FCF8F<F8F8*(,(**F1F8F9F8FEF8
F@F8F8**FCF8F<F8FFF8F@F8F8*(FCF8FEF8FJF8F8F8FCF8FEF8F8*&,&*(FCF8F9F8F@
F8FH*&F1F8FJF8F8F8F1F8F8,(*(F/F8F1F8F<F8F8*(FMF8F1F8FEF8F8*&FRF8FCF8FH
,&*&F/F8FEF8FH*&FMF8F<F8F8" }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0
 "" {MPLTEXT 1 202 25 "Vitesse:=map(simplify,V);" }{MPLTEXT 1 202 0 ""
 }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I(VitesseG6\"-I'vectorG6$I*protec
tedGF)I(_syslibGF%6#7%-I%diffGF)6$-I$rhoGF%6#I\"tGF%F3*&-F.6$-I&thetaG
F%F2F3\"\"\"F0F9*(-I$sinGF(6#F7F9-F.6$-I$phiGF%F2F3F9F0F9" }{TEXT 204 
0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 100 "A:=vector([dotp
rod(a,ur,'orthogonal'),dotprod(a,utheta,'orthogonal'),dotprod(a,uphi,'
orthogonal')]);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" {XPPMATH 20 
"6#>I\"AG6\"-I'vectorG6$I*protectedGF)I(_syslibGF%6#7%,(*(,2**-I$sinGF
(6#-I&thetaGF%6#I\"tGF%\"\"\"-I%diffGF)6$F4F7\"\"#-I$cosGF(6#-I$phiGF%
F6F8-I$rhoGF%F6F8!\"\"**-F>F3F8-F:6$F4-I\"$GF)6$F7F<F8F=F8FBF8F8*,FFF8
F9F8-F2F?F8-F:6$F@F7F8FBF8!\"#**FFF8F9F8F=F8-F:6$FBF7F8F<**F1F8F=F8FNF
<FBF8FD**F1F8FMF8-F:6$F@FIF8FBF8FD**F1F8FMF8FNF8FRF8FP*(F1F8F=F8-F:6$F
BFIF8F8F8F1F8F=F8F8*(,2**F1F8F9F<FMF8FBF8FD**FFF8FGF8FMF8FBF8F8*,FFF8F
9F8F=F8FNF8FBF8F<**FFF8F9F8FMF8FRF8F<**F1F8FMF8FNF<FBF8FD**F1F8F=F8FVF
8FBF8F8**F1F8F=F8FNF8FRF8F<*(F1F8FMF8FZF8F8F8F1F8FMF8F8*&,**(FFF8F9F<F
BF8FD*(F1F8FGF8FBF8FD*(F1F8F9F8FRF8FP*&FFF8FZF8F8F8FFF8F8,(*(F/F8FFF8F
=F8F8*(FgnF8FFF8FMF8F8*&FaoF8F1F8FD,&*&F/F8FMF8FD*&FgnF8F=F8F8" }
{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 30 "Accele
ration:=map(simplify,A);" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#>I-AccelerationG6\"-I'vectorG6$I*protectedGF)I(_syslibG
F%6#7%,**(-I%diffGF)6$-I$phiGF%6#I\"tGF%F5\"\"#-I$rhoGF%F4\"\"\"-I$cos
GF(6#-I&thetaGF%F4F6F9-F06$F7-I\"$GF)6$F5F6F9*&-F06$F=F5F6F7F9!\"\"*&F
/F6F7F9FG,(**F:F9-I$sinGF(F<F9F/F6F7F9FG*&-F06$F=FAF9F7F9F9*&FEF9-F06$
F7F5F9F6,(**F:F9FEF9F/F9F7F9F6*(FKF9-F06$F2FAF9F7F9F9*(FKF9F/F9FQF9F6"
 }{TEXT 204 0 "" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 202 0 "" }}}
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