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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "# HONEY BEE, spirali
ng in toward the origin FOWLES Example 1.11.1" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "alpha:=1:          r0 :=5:   v0:= -0.5:  " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "a:=0: w0:=0: theta0:=0:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "# radial : r0=position v0=ve
locity a=acceleration" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "# \+
angular : alpha=acceleration w0=initial velocity theta0=initial angle
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "r:=r0+v0*t+0.5*a*t*t:  \+
   theta:=theta0+w0*t+0.5*alpha*t*t:     # radial/angular variables" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "myx := r*cos(theta): myy :
= r*sin(theta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "rdot :=
 diff(r,t): rddot := diff(rdot,t): thetadot := diff(theta,t): thetaddo
t := diff(thetadot,t):# time derivatives" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 100 "tmax := fsolve(r=0,t,t=0.0..10000000);  # solve for \+
when bee hits origin - stop graphs at that point" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 80 "vmag := sqrt( (rdot)^2 + (r*thetadot)^2 ) : v
ang :=  (r*thetadot); vrad := rdot:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "amag := sqrt( (rddot-r*(thetadot^2))^2 + (r*thetaddot
+2*rdot*thetadot)^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "aa
ng := r*thetaddot+2*rdot*thetadot: arad := rddot-r*(thetadot^2):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "vmax := eval(vmag,t=fsolve(
 diff(vmag,t)=0,t,t=0.0001..tmax)); time_for_vmax := fsolve( diff(vmag
,t)=0,t,t=0.0001..tmax);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 
"plot([myx,myy,t=0..tmax],thickness=2,numpoints=200,title=\"Overhead P
ath of Bee (x vs y)\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 174 
"plot([vrad,vang,vmag],t=0..tmax,thickness=2,numpoints=200,color=[blue
,yellow,green],labels=[\"t\",\"|V|\"],legend=[\"V_radial\",\"V_angular
\",\"V_total\"],title=\"Velocity components\");" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 178 "plot([arad,aang,amag],t=0..tmax,thickness=2,n
umpoints=200,color=[blue,yellow,green],labels=[\"t\",\"|A|\"],legend=[
\"A_radial\",\"A_angular\",\"A_total\"],title=\"Acceleration component
s\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "plot([vang,aang],
t=0..tmax,thickness=2,numpoints=200,legend=[\"V_angular\",\"A_angular
\"],color=[blue,red],labels=[\"t\",\"v and a (angular)\"]);" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 227 "#  Note : Looking at the last plot above ... the zero for the a
ngular acceleration does NOT occur at the peak of the angular velocity
 curve!!!  (we have to take into account the rotation of the radial an
d angular unit vectors!)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }
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