Experimental Mathematics 1 (2010)
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#contents
* Á°²ó¤Î²ÝÂê¤Ë¤Ä¤¤¤Æ [#t35efe13]
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¤Þ¤º¡¤±ôľ²¼Êý¸þ¤«¤é¤Î³ÑÅÙ¤ò θ rad ¤È¤¹¤ë¤È Newton ...
CENTER:&ref(./pendulum-eq.png,70%);
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CENTER:&ref(./pendulum-euler.png,70%);
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// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# Euler Ë¡¤Ë´ð¤Å¤¤¤Æ¡¤¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
def euler(u,v,dt,l)
g = 9.8
u_new = u + v*dt
v_new = v - (g/l)*sin(u)*dt
return u_new, v_new
end
# x, y¤ò½ÐÎϤ¹¤ë
def outputXY(u,l)
x = l*sin(u)
y = - l*cos(u)
print(x,", ",y,"\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ÌäÂê¾ò·ï
l = 1.0
# ½é´üÃÍ
u = PI/3.0
v = 0.0
time = 0.0
# ½ªÎ»»þ´Ö
t_limit = 5.0
# »þ´Ö¹ï¤ßÉý
dt = 0.01
# ½ªÎ»»þ´Ö¤Þ¤Ç¤Ï·×»»¤ò·«¤êÊÖ¤¹
while (time < t_limit) do
# x, y ¤ò½ÐÎÏ
outputXY(u,l)
# Euler Ë¡¤Ç¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
u,v = euler(u,v,dt,l)
# »þ´Ö¤ò¹¹¿·
time += dt
end
}}
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¤Þ¤º¤ÏÀßÄê¥Õ¥¡¥¤¥ëËÜÂΤò ''pendulum.plt'' ¤È¤·¤Æ
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[-1.0:1.0]
set yrange[-1.0:0.0]
set xlabel "x"
set ylabel "y"
unset key
line=0
load "pendulum.loop"
}}
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// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
plot "pendulum.dat" every ::line::line w p pt 6 ps 3
line=line+1
pause 0.01
if(line<501) reread
}}
¤³¤ì¤Ç gnuplot ¾å¤Ç
load "pendulum.plt"
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&br;
&ref(/materials/warning.png); 1¹Ô¤º¤Ä¤Î¥°¥é¥Õ¤ò²èÁü¥Õ¥¡¥¤...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[-1.0:1.0]
set yrange[-1.0:0.0]
set xlabel "x"
set ylabel "y"
unset key
set terminal png font arial 18 size 800,600
line=0
load "pendulum.loop"
set terminal win
set output
}}
¤È¤·¡¤¥ë¡¼¥×Éôʬ¤ÎÀßÄê¥Õ¥¡¥¤¥ë ''pendulum.loop'' ¤ò
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
op = sprintf("p-%03d.png",line)
set output op
plot "pendulum.dat" every ::line::line w p pt 6 ps 3
line=line+1
if(line<501) reread
}}
¤Ê¤É¤È¤¹¤ì¤Ð¡¤gnuplot ¤Ç
load "pendulum.plt"
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&br;
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** ''¾ò·ï'' [#v4c1199c]
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&br;
** ''Äó½Ð¤Ë¤Ä¤¤¤Æ'' [#rcae66a5]
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// (&ref(/materials/JNorth_arrow-right-sm.png);&ref(./que...
* about Icons, ClipArts [#w04c90f9]
Some icons in this page are downloadable at [[ICONFINDER:...
The "note" icon &ref(/materials/notes.png); designed by [...
the "warning" icon &ref(/materials/warning.png); designed...
and the "triangle" icon &ref(/materials/JNorth_arrow-righ...
Some clip arts used in this page are downloadable at [[Op...
We deeply appreciate their superb works. With licence, th...
// ¨¬¨¨®¨¯¨°¨±¨²¨³¨´¨µ¨¶
// ¥³¥Þ¥ó¥É¥é¥¤¥óÆþÎϤϡֹÔƬ¤ò¥Ö¥é¥ó¥¯¤Ç»Ï¤á¤ë¡×.
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// &ref(/materials/notes.png);
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// CENTER:&size(24){''¤Û¤²¤Û¤²''};
// programu source ɽµ
// #highlighter(language=ruby,number=on,cache=on){{}}
½ªÎ»¹Ô:
#contents
* Á°²ó¤Î²ÝÂê¤Ë¤Ä¤¤¤Æ [#t35efe13]
¤µ¤Æ¡¤Á°²ó¤ÎÁí»Å¾å¤²¤Ïñ½ã¤Ê¿¶¤ê»Ò¤Î±¿Æ°¤ò¥·¥ß¥å¥ì¡¼¥·¥ç...
¤Þ¤º¡¤±ôľ²¼Êý¸þ¤«¤é¤Î³ÑÅÙ¤ò θ rad ¤È¤¹¤ë¤È Newton ...
CENTER:&ref(./pendulum-eq.png,70%);
CENTER:''¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°''
¤Ëµ¢Ã夹¤ë¤Î¤Ï¹â¹»¤ÎʪÍý¤Î¼ø¶È¤Ç¤ä¤Ã¤Æ¤¤¤ë¤Ï¤º¤À(¿Í¤Ë¤è¤Ã...
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CENTER:&ref(./pendulum-eq-mod.png,70%);
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¤È¤¤¤¦´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¡¥¤½¤·¤Æ¡¤¾å¤ÎÊýÄø¼°¤ËÂФ·¤Æ Euler ...
CENTER:&ref(./pendulum-euler.png,70%);
CENTER:''¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°(ÊÑ·ÁÈǤΠEuler Ë¡¤Ë¤è¤ë¶á»÷)''
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CENTER:&ref(./pendulum-euler-mod.png,70%);
CENTER:''¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°(ÊÑ·ÁÈǤΠEuler Ë¡¤Ë¤è¤ë¶á»÷¤ò...
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// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# Euler Ë¡¤Ë´ð¤Å¤¤¤Æ¡¤¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
def euler(u,v,dt,l)
g = 9.8
u_new = u + v*dt
v_new = v - (g/l)*sin(u)*dt
return u_new, v_new
end
# x, y¤ò½ÐÎϤ¹¤ë
def outputXY(u,l)
x = l*sin(u)
y = - l*cos(u)
print(x,", ",y,"\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ÌäÂê¾ò·ï
l = 1.0
# ½é´üÃÍ
u = PI/3.0
v = 0.0
time = 0.0
# ½ªÎ»»þ´Ö
t_limit = 5.0
# »þ´Ö¹ï¤ßÉý
dt = 0.01
# ½ªÎ»»þ´Ö¤Þ¤Ç¤Ï·×»»¤ò·«¤êÊÖ¤¹
while (time < t_limit) do
# x, y ¤ò½ÐÎÏ
outputXY(u,l)
# Euler Ë¡¤Ç¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
u,v = euler(u,v,dt,l)
# »þ´Ö¤ò¹¹¿·
time += dt
end
}}
Î㤨¤Ð¤³¤Î¥×¥í¥°¥é¥à¤òÆ°¤«¤»¤Ð¡¤Á´Éô¤Ç 501 ¹Ô¤È¤Ê¤ë¥Ç¡¼¥¿...
¤Þ¤º¤ÏÀßÄê¥Õ¥¡¥¤¥ëËÜÂΤò ''pendulum.plt'' ¤È¤·¤Æ
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[-1.0:1.0]
set yrange[-1.0:0.0]
set xlabel "x"
set ylabel "y"
unset key
line=0
load "pendulum.loop"
}}
¤ÈÍÑ°Õ¤·¡¤¤µ¤é¤Ë1¹Ô¤º¤Ä¥°¥é¥Õ¤ò½ñ¤¯Éôʬ¤Î¤¿¤á¤Î¥Õ¥¡¥¤¥ë '...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
plot "pendulum.dat" every ::line::line w p pt 6 ps 3
line=line+1
pause 0.01
if(line<501) reread
}}
¤³¤ì¤Ç gnuplot ¾å¤Ç
load "pendulum.plt"
¤È¤¹¤ì¤Ð(¤½¤³¤½¤³Â®¤¤ PC ¤Ê¤é¤Ð) ¸½¼Â¤È¤Û¤ÜƱ¤¸Æ°ºî¤ò²èÌÌ...
&br;
&ref(/materials/warning.png); 1¹Ô¤º¤Ä¤Î¥°¥é¥Õ¤ò²èÁü¥Õ¥¡¥¤...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[-1.0:1.0]
set yrange[-1.0:0.0]
set xlabel "x"
set ylabel "y"
unset key
set terminal png font arial 18 size 800,600
line=0
load "pendulum.loop"
set terminal win
set output
}}
¤È¤·¡¤¥ë¡¼¥×Éôʬ¤ÎÀßÄê¥Õ¥¡¥¤¥ë ''pendulum.loop'' ¤ò
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
op = sprintf("p-%03d.png",line)
set output op
plot "pendulum.dat" every ::line::line w p pt 6 ps 3
line=line+1
if(line<501) reread
}}
¤Ê¤É¤È¤¹¤ì¤Ð¡¤gnuplot ¤Ç
load "pendulum.plt"
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** ''²ÝÂê'' [#e9160035]
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** ''¾ò·ï'' [#v4c1199c]
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&br;
** ''Äó½Ð¤Ë¤Ä¤¤¤Æ'' [#rcae66a5]
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// (&ref(/materials/JNorth_arrow-right-sm.png);&ref(./que...
* about Icons, ClipArts [#w04c90f9]
Some icons in this page are downloadable at [[ICONFINDER:...
The "note" icon &ref(/materials/notes.png); designed by [...
the "warning" icon &ref(/materials/warning.png); designed...
and the "triangle" icon &ref(/materials/JNorth_arrow-righ...
Some clip arts used in this page are downloadable at [[Op...
We deeply appreciate their superb works. With licence, th...
// ¨¬¨¨®¨¯¨°¨±¨²¨³¨´¨µ¨¶
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// &ref(/materials/warning.png);
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// &ref(/materials/JNorth_arrow-right-sm.png);
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// programu source ɽµ
// #highlighter(language=ruby,number=on,cache=on){{}}
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