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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "This example is a simple L
issajous figure, slowed down sufficiently" }}{PARA 0 "" 0 "" {TEXT -1 
62 "(after trial and error) so that the arrows won't get too long." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 27 "r:=[sin(2*t/5),sin(3*t/5)];" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 63 "A tiny useful command: op, take a look at the h
elp pages!   ?op" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(r);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "This is our curve." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 66 "curve:=plot([op(r),t=0..2*Pi*5],color=blue,thi
ckness=1,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "curv
e;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Sloppy work -- no vectors h
ere, just lists. We do not need the map command." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "v:=diff(r,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "a:=diff(v,t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Followin
g is a naive small procedure that draws short line segments" }}{PARA 
0 "" 0 "" {TEXT -1 69 "at the appropriate points. As we are working wi
th lists (not vectors)" }}{PARA 0 "" 0 "" {TEXT -1 66 "we add the comp
onents manually. Similarily, as we have expressions" }}{PARA 0 "" 0 "
" {TEXT -1 48 "(not functions), we need to substitute t-values." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "arrows:=proc(tt);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "     base:=subs(t=tt,r);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "     vtt:=subs(t=tt,v);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "     att:=subs(t=tt,a);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "     vtip:=[base[1]+vtt[1],base[2]+vtt[2]];" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 43 "     atip:=[base[1]+att[1],base[2]+att[2]
];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "    arr1:=plot([base,vtip],th
ickness=2,color=green):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "    arr2
:=plot([base,atip],thickness=2,color=red);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "    display(\{arr1,arr2\});" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Cleaner p
rogramming would use the local command (?command)" }}{PARA 0 "" 0 "" 
{TEXT -1 63 "to declare the local vraiables to be used inside the proc
edure." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 
"Two times 12 arrows all shown at the same time. Their spacing was" }}
{PARA 0 "" 0 "" {TEXT -1 69 "fine-tuned by hand. Also, as in the first
 try they all were too long," }}{PARA 0 "" 0 "" {TEXT -1 66 "and I was
n't in the mood to program some fancy automatic rescaling" }}{PARA 0 "
" 0 "" {TEXT -1 71 "I just reparameterized the original curve so that \+
it is traced out more" }}{PARA 0 "" 0 "" {TEXT -1 45 "slowly (see the \+
fives in the defintion of r)." }}{PARA 0 "" 0 "" {TEXT -1 69 "A nice p
rogram would create this animation in one step, automatically" }}
{PARA 0 "" 0 "" {TEXT -1 71 "from the data defining r in the first lin
e above. The only tricky parts" }}{PARA 0 "" 0 "" {TEXT -1 63 "are the
 automatic rescaling, and a few other aesthetic details." }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "display(\{curve,seq(arrows(2.5*i),i=1..12)\});" }}}
{EXCHG {PARA 258 "" 0 "" {TEXT -1 69 "Use the buttons on the toolbar t
o set the disaply to \"looping around\"" }}{PARA 259 "" 0 "" {TEXT -1 
57 "and to reduce the fram-per-seconds rate as needed. Enjoy!" }}
{PARA 260 "" 0 "" {TEXT 256 10 "Questions:" }}{PARA 261 "" 0 "" {TEXT 
-1 55 "(a) Where is the acceleration parallel to the velocity?" }}
{PARA 262 "" 0 "" {TEXT -1 29 "(b) Where are they othogonal?" }}{PARA 
263 "" 0 "" {TEXT -1 43 "(c) Is the acceleration ever equal to zero?" 
}}{PARA 264 "" 0 "" {TEXT -1 46 "(d) When does it point forward, when \+
backward?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "display([seq(display(
\{curve,arrows(.5*i)\}),i=1..63)],insequence=true);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "12" 0 }{VIEWOPTS 1 1 0 1 1 
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