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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "rotvecs.mws    8/30/95" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 165 "A 'start
er' program in maple release 4 to show how one can animate rotating an
d coounter-rotating vectors to obtain a combination which is a linearl
y polarized wave." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 489 "This is to  help in the writing of a program which adds \+
a clockwise and counterclockwise circularly-polarized wave as they tra
vel into a medium where the two circular polarizations have different \+
wavelengths.  The new program should show linear polarization along th
e x-axis (as this program does) when x=0.   As x > 0, the program shou
ld show that the two circular polarizations add together along a line \+
which is at an angle to the x-axis.  The this angle to the x-axis incr
eases with x." }}{PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"with(plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Qx is the x-comp
onent of both the CW and CCW rotating waves." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "Qx:=5.0*cos(3*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "Qy2:=5.0*sin(-3*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "Qy1:=5.0 * sin(3*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "Nframes:=20;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "for i from 0 to Nframes  do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "j:=2/Nframes;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "g.(i):=plot(su
bs(t=i*j,[[0,0],[Qx,Qy1]]),color='red',thickness=3):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "h.(i):=plo
t(subs(t=i*j,[[0,0],[Qx,Qy2]]),color='blue',thickness=3):" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 75 "j.(i):=plot(subs(t=i*j,[[0,0],[Qx+Qx,Qy1+Qy2
]]),color='black',thickness=5):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "
k.(i):=display(\{g.(i),h.(i),j.(i)\}):" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 3 "od:" }}}{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 42 "display([k.(0..Nframes)],insequence=true);" }}}}
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