Experimental Mathematics 1 (2010)
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#contents
* Á°²ó¤Î²ÝÂê¤Ë¤Ä¤¤¤Æ [#z81ce357]
Á°²ó¤ÎÁí»Å¾å¤²¤Ï¡¤Í¿¤¨¤é¤ì¤¿ÃÏ¿Þ¤ÎÆóÅÀ´Ö¤ÇºÇû·ÐÏ©¤òÆ»¤¬...
(ÃϿޤˤĤ¤¤Æ¤ÏÁ°²ó¤Î web ¤ò»²¾È¤Î¤³¤È)
¿Þ¤¬Èó¾ï¤ËÁÇľ¤Ç´Êñ¤Ê·Á¤ò¤·¤Æ¤¤¤ë¤Î¤Ç¡¤ºÇû·ÐÏ©¤Î¸Ä¿ô¤ò...
¶ñÂÎŪ¤Ë¤Ï¡¤
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¡Ö¤¢¤ëÅÀ¤òÄ̤ëºÇû·ÐÏ©¤Ï¡¤¤½¤Î¾å¤ÎÅÀ¤«±¦¤ÎÅÀ¤òÄ̤äƤä¤Ã...
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Î㤨¤ÐÃÏ¿Þ¤òÁÇľ¤Ë x,y ºÂɸ¤Ç°Ê²¼¤Î¤è¤¦¤ËÆÃħÉÕ¤±¤¿¤È¤·¤Æ¡¤
CENTER:&ref(./route-exp.png,70%);
¤Î¤è¤¦¤Ë¹Í¤¨¤¿¤È¤·¤è¤¦¡¥
¤³¤Î¤È¤¡¤ºÂɸ (i,j) (0 ≤ i ≤ 6, 0 ≤ j ≤ 4)¤Î...
CENTER:&ref(./map-eq-1.png);
¤È¤Ê¤ë¤Î¤Ç¡¤¤³¤ì¤ò»È¤¨¤Ð¤è¤¤¡¥¤¢¤È¤Ï¡¤¤³¤Î´Ø·¸¼°¤òÅú¤¨¤Ë...
¤Ê¤ª¡¤¾å¤Î¼°¤òÅÓÃæ¤Þ¤Ç¼ê¤ÇŸ³«¤·¤¿·Á¤Î
CENTER:&ref(./map-eq-2.png);
¤ò»È¤Ã¤Æ¤âÎɤ¤¡¥¤¿¤À¡¤¤³¤¦¤¤¤¦¤è¤¦¤Ë¡Ö¿Í´Ö¤¬ÅÓÃæ¤Þ¤Ç²ðÆþ...
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** ºÆµ¢ÄêµÁ¤ò»È¤¦¾ì¹ç [#q58a3e88]
¤³¤ì¤Ï¿ô¼°¤òÁÇľ¤Ë»È¤¨¤Ð¤è¤¤¤Î¤Ç¡¤Î㤨¤Ð°Ê²¼¤Î¤è¤¦¤Ë¤Ê¤ë...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# f ¤òµá¤á¤ëºÆµ¢ÄêµÁ¼°
def f(i,j)
if ((i==6) && (j==4)) then
return 1
elsif (j==4) then
return f(i+1,4)
elsif (i==6) then
return f(6,j+1)
else
return f(i+1,j) + f(i, j+1)
end
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# f(0,0) ¤ÎÃͤò½ÐÎϤ¹¤ë¡¥
print(f(0,0),"\n")
}}
&br;
** ưŪ·×²èË¡¤â¤É¤¤ò»È¤¦¾ì¹ç [#ge33c2ea]
±¦¾å¤Î Start ÃÏÅÀ¤«¤é¡¤¡Ö²¿¥¹¥Æ¥Ã¥×Ìܤ«¡×¤È¤¤¤¦¤³¤È¤ËÃåÌÜ...
CENTER:&ref(./route-exp-2.png,70%);
¾¯¤·¹©Éפ¬¤¤¤ë¤¬¡¤¤Þ¤¢Î㤨¤Ð¼¡¤Î¤è¤¦¤Ë¥×¥í¥°¥é¥à¤ò½ñ¤±¤ë...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# step ¤Î¾®¤µ¤¤¤Û¤¦¤«¤é·×»»¤·¤Æ¤¤¤Ã¤Æ¡¤Goal ¤Ç¤ÎÃͤòÊÖ¤¹....
def calc_top(nx,ny)
# ³ÆÅÀ¤òÄ̤ëºÇû·ÐÏ©¿ô¤òµÏ¿¤·¤Æ¤ª¤¯ÇÛÎó¤òÍÑ°Õ¤·¤è¤¦¡¥
f = Array.new(nx+1){ Array.new(ny+1){ 0 } }
# Start ÃÏÅÀ¤Ç¤Î f ¤Ï 1 ¤À¤Í¡¥
f[nx][ny] = 1
# Áí¥¹¥Æ¥Ã¥×¿ô
all_step = nx + ny
# step 1 ¤«¤é all_step ¤Þ¤Ç
for step in 1..all_step do
# Ʊ¤¸ step ¤ÎÅÀ¤Ï x + y = all_step - step ¤òËþ¤¿¤¹...
for i in 0..(all_step - step) do
j = (all_step - step) - i
if ((0 <= i) && (i <= nx) && (0 <= j) && (j <= ny))...
# ¤¢¤È¤ÏÉáÄ̤˷׻»¤¹¤ë
if (i==nx) then
f[i][j] = f[i][j+1]
elsif (j==ny) then
f[i][j] = f[i+1][j]
else
f[i][j] = f[i+1][j] + f[i][j+1]
end
end
end
end
# f(0,0) ¤òÊÖ¤¹¡¥
return f[0][0]
end
# Goal ¤Ç¤Î f ¤ÎÃͤò·×»»¤¹¤ë
ans = calc_top(6,4)
# ÃΤꤿ¤¤Ãͤòɽ¼¨¤¹¤ë
print(ans,"\n")
}}
** ¾¯¤·¸¤¤¹Í¤¨Êý [#ec4aa7e8]
ºÇû·ÐÏ©¿ô¤Î°Í¸´Ø·¸¤ò¹Í¤¨¤ë¤È¡Ö±¦¾å¤«¤éº¸²¼¤Ë¼Ð¤á¡×¤ËÏÃ...
¸À¤¤´¹¤¨¤ë¤È¡¤¡Ö¤³¤Î¼Ð¤á¤ÎÊý¸þ¤¬ÁÇľ¤ÊÊý¸þ¡×¤Ë¤Ê¤ë¤Î¤Ç¡¤...
¼ÂºÝ¤Ë·¹¤±¤Æ¤ß¤è¤¦¡¥
¤¹¤ë¤È¡¤°Í¸´Ø·¸¤¬Á°²ó¤Î¡ÖÌÚ¹½Â¤¡×¤Î¤È¤³¤í¤Ç¤ä¤Ã¤¿ÏäÈÁ´...
¤½¤³¤Ç¡¤¤¿¤È¤¨¤ÐÁ´ÂΤ¬¡Ö¤ï¤«¤ê¤ä¤¹¤¤ÌÚ¹½Â¤¡×¤Ë¤Ê¤ë¤è¤¦¤Ë...
CENTER:&ref(./route-tree.png,60%);
¤¢¤È¤Ï¡¤²¼¤Î¿ô»ú¤ò¤¹¤È¼«Ê¬¤Î¿ô»ú¤Ë¤Ê¤ë¡¤¤È¤¤¤¦»ÅÁȤߤò...
¤³¤ì¤Ç¹Í¤¨¤ë¤È¡¤Æ°Åª·×²èË¡¤â¤É¤¤Î¥×¥í¥°¥é¥ß¥ó¥°¤â¾å¤È°ã...
·×»»Î̤ÏÁý¤¨¤ë¤¬¡¤¤³¤¦¤·¤¿ÁÇľ¤Ê¥×¥í¥°¥é¥à¤Ë¤Ï¥ß¥¹¤¬Æþ¤ë...
Åú¤¨¤¬´Ö°ã¤Ã¤Æ¤¤¤ì¤Ð°ÕÌ£¤¬Ìµ¤¤¤Î¤À¤«¤é¡¤¤Þ¤º¤Ï¤³¤¦¤·¤¿¡Ö...
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CENTER:&size(24){''°Í¸´Ø·¸¤Ê¤É¤ò¤è¤¯¹Í¤¨¤Æ¡¤''};
CENTER:&size(24){''»öÁ°¤ËÌäÂꤽ¤Î¤â¤Î¤ò½èÍý¤·¤ä¤¹¤¤·Á¤ËÍý...
CENTER:&size(24){''¥×¥í¥°¥é¥ß¥ó¥°¤Ë¤Ï½ÅÍפǤ¢¤ë¡¥''};
&br;
* Áí¹çÎÏ: ÈùʬÊýÄø¼°¤ò²ò¤¤¤Æ, ²ò¤ò¸«¤Æ¤ß¤è¤¦ [#u0bdf45e]
¤³¤ì¤Þ¤Ç¤Ç¥×¥í¥°¥é¥ß¥ó¥°¤Ë¤Ä¤¤¤Æ''ºÇÄã¸Â''¤ÎÃμ±¤Ï¿È¤Ë¤Ä...
¤¤¤í¤ó¤ÊÂêºà¤¬¤¢¤ë¤¬¡¤¤Þ¤º¤Ï¤´¤¯´Êñ¤Ê¾ïÈùʬÊýÄø¼°¤ËÂФ·...
&br;
** ¼«Í³Íî²¼¤ò¥·¥ß¥å¥ì¡¼¥È¤·¤Æ¤ß¤ë [#w4302938]
³ØÀ¸¤¬ºÇ¤â¤è¤¯ÃΤäƤ¤¤ë¾ïÈùʬÊýÄø¼°¤Ç¤¢¤ë¡¤Newton ÎϳؤË...
¤Þ¤º¤â¤Ã¤È¤â´Êñ¤Ê¡¤¡Ö¿¿¶õÃæ¤òʪÂΤ¬¼«Í³Íî²¼¤·¤Æ¤¯¤ëÍÍ»Ò...
»þ´Ö¤ò t sec, ÃϾ夫¤é¤ÎʪÂΤι⤵¤ò u(t) m¡¤½ÅÎϲîÅÙ g...
Newton ¤Î±¿Æ°ÊýÄø¼° F = ma ¤è¤ê¡¤
CENTER:&ref(./newton.png,70%);
CENTER:''ʪÂΤι⤵¤Ë¤Ä¤¤¤Æ¤Î¾ïÈùʬÊýÄø¼°''
¤È¤¤¤¦¾ïÈùʬÊýÄø¼°¤¬ÆÀ¤é¤ì¤ë¡¥
¤³¤ì¤ÏÆ󳬾ïÈùʬÊýÄø¼°¤Ç¾¯¤·°·¤¤¤Ë¤¯¤¤¤Î¤Ç¡¤Â®ÅÙ v = du/d...
CENTER:&ref(./newton-2.png,70%);
CENTER:''ʪÂΤι⤵¤Ë¤Ä¤¤¤Æ¤Î¾ïÈùʬÊýÄø¼°(ÊÑ·ÁÈÇ)''
¤È¤¤¤¦¤â¤Î¤ËÊÑ·Á¤·¤Æ¡¤¤³¤ì¤Ë¤Ä¤¤¤Æ¹Í¤¨¤è¤¦¡¥
¤³¤ÎÊýÄø¼°¤Ï¼ê¤Ç²ò¤±¤Æ¤·¤Þ¤¦¤¬¡¤¼ê¤Ç¸·Ì©²ò¤¬µá¤Þ¤é¤Ê¤¤¾ì...
&br;
*** Euler Ë¡ [#q2524109]
Euler Ë¡¤È¤¤¤¦¤Î¤Ï´Êñ¤Ç¡¤»þ´ÖȯŸ¹à¤òÁ°¿Êº¹Ê¬¤Ç¶á»÷¤¹¤ë...
¤Þ¤¢¡¤ÍýÏÀ¤ò¸À¤¦¤è¤ê¸«¤¿¤Û¤¦¤¬Áᤤ¤À¤í¤¦¡¥
º£²ó¤Î¾ì¹ç¡¤»þ´ÖÊÑ¿ô t ¤ò ¢¤t ¤ÎÉý¤Ç¡Ö¹ï¤à¡×¤³¤È¤Ë¤·¤Æ¡¤¾å...
CENTER:&ref(./euler.png,70%);
CENTER:''¾å¤Î¾ïÈùʬÊýÄø¼°¤ò Euler Ë¡¤Ç¡Ö¶á»÷¡×¤·¤¿¤â¤Î''
¤È¤¹¤ë¤Î¤¬ Euler Ë¡¤Ç¤¢¤ë¡¥¤½¤·¤Æ¤³¤Î¼°¤ò¤¤ì¤¤¤Ë½ñ¤Ä¾¤¹...
CENTER:&ref(./euler-2.png,70%);
CENTER:''¾å¤Î¾ïÈùʬÊýÄø¼°¤ò Euler Ë¡¤Ç¡Ö¶á»÷¡×¤·¤¿¤â¤Î(º¸...
¤È¤Ê¤ë¤Î¤Ç¡¤¤³¤ì¤ò¤ß¤ë¤È¡Ö±¦ÊÕ¤ËÃΤäƤ¤¤ëÃͤòÂåÆþ¤¹¤ë¤À...
¾ïÈùʬÊýÄø¼°¤ò¤³¤Î¤è¤¦¤Ë¶á»÷¼°¤ËÃÖ¤´¹¤¨¤ë¤Î¤¬ Euler Ë¡¤Ç...
¤³¤ì¤Ê¤é¥×¥í¥°¥é¥à¤¬½ñ¤±¤½¤¦¤À¤È¤¤¤¦´¶¿¨¤¬ÆÀ¤é¤ì¤ë¤À¤í¤¦¡¥
&br;
&ref(/materials/warning.png); ¤â¤Á¤í¤ó¡¤Euler Ë¡¤Çºî¤Ã¤¿...
&br;
*** ÌäÂêÀßÄê [#o50d4c8e]
¤µ¤Æ¡¤¥·¥ß¥å¥ì¡¼¥È¤¹¤ë¤Ë¤Ï¶ñÂÎŪ¤Ê¾ò·ï¤òµÍ¤á¤Ê¤¤¤È¤¤¤±¤Ê...
¤½¤³¤Ç¡¤°Ê²¼¤Î¤è¤¦¤Ë½é´ü¾ò·ï¤Ê¤É¤òÀßÄꤷ¤è¤¦¡¥
''[½é´ü¾ò·ï]''
½é´ü¹â¤µ u(0) = 1000.0 (m)
½é´ü®ÅÙ v(0) = 0.0 (m/s)
''[½ªÎ»¾ò·ï]''
¹â¤µ¤¬ 0 m°Ê²¼¤È¤Ê¤Ã¤¿¤é¥·¥ß¥å¥ì¡¼¥·¥ç¥ó½ªÎ».
''[¶á»÷¾ò·ï]''
»þ´Ö¹ï¤ßÉý ¢¤t = 0.1 sec
&br;
*** ¥×¥í¥°¥é¥à [#d15c251c]
// ¼Â½¬¥¢¥¤¥³¥ó
&ref(/materials/notes.png); °Ê²¼¤ÎÉôʬ¤Ï¼Â½¬¤·¤Ê¤¬¤éÍý²ò...
&br;
¥×¥í¥°¥é¥à¤Ï¾å¤Î¾ò·ï¤Ë½¾¤Ã¤Æ·×»»¤·¤Æ »þ´Ö, ¹â¤µ ¤Î¿ô»ú¥Ú...
¤¹¤ë¤È¡¤¤À¤¤¤¿¤¤°Ê²¼¤Î¤è¤¦¤Ê´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¤«¡¥
// 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)
g = 9.8
u_new = u + v*dt
v_new = v - g*dt
return u_new, v_new
end
# »þ´Ö¤È¹â¤µ¤ò½ÐÎϤ¹¤ë
def output(u, time)
print(time,", ",u,"\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ½é´üÃÍ
u = 1000.0
v = 0.0
time = 0.0
# »þ´Ö¹ï¤ßÉý
dt = 0.1
# ¹â¤µ u ¤¬Àµ¤Î¤¦¤Á¤Ï·×»»¤ò·«¤êÊÖ¤¹
while (u > 0) do
# ¹â¤µ¤È»þ´Ö¤ò½ÐÎÏ
output(u, time)
# Euler Ë¡¤Ç¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
u,v = euler(u,v,dt)
# »þ´Ö¤ò¹¹¿·
time += dt
end
}}
&br;
*** ¥×¥í¥°¥é¥à¤òÆ°¤«¤·¤Æ¥Ç¡¼¥¿¤òÆÀ¤ë [#r786047b]
¾å¤Î¥×¥í¥°¥é¥à¤ò¼Â¹Ô¤·¤Æ¡¤¥Ç¡¼¥¿¤òÆÀ¤è¤¦¡¥ÆÀ¤é¤ì¤¿¥Ç¡¼¥¿...
¤½¤ì¤Ë¤ÏÎ㤨¤Ð¡¤¾å¤Î¥×¥í¥°¥é¥à¥Õ¥¡¥¤¥ë̾¤¬ euler.rb ¤À¤È...
ruby -w euler.rb > euler.dat
¤Ê¤É¤È¤·¤Æ¼Â¹Ô¤¹¤ì¤Ð¤è¤¤¡Ä¤Î¤Ï³Ð¤¨¤Æ¤¤¤ë¤Í¡© ¤³¤Î¾ì¹ç¡¤¥Ç...
&br;
*** ÆÀ¤é¤ì¤¿¥Ç¡¼¥¿¤òÆ°²èŪ¤Ë¸«¤Æ¤ß¤è¤¦ [#h76da810]
¾å¤Î¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë¤ò¸«¤Æ¤ß¤ë¤È¡¤Á´Éô¤Ç 144¹Ô¤¢¤ë¡¥¤½¤³¤Ç...
¤½¤³¤Ç¡¤°Ê²¼¤Î¤è¤¦¤Ëºî¶È¤·¤Æ¤ß¤è¤¦¡¥
&br;
1) gnuplot ¤ÎÆ°ºî¥Õ¥¡¥¤¥ë¤òºî¤ë: ''euler.plt'' ¤È¤¤¤¦Ì¾...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[0:15]
set yrange[0:1000]
set xlabel "Time"
set ylabel "Height"
unset key
line=0
load "euler.loop"
}}
&br;
2) gnuplot ¤ÎÆ°ºî¥Õ¥¡¥¤¥ë¤òºî¤ë(1¹Ô¤º¤Äɽ¼¨¤¹¤ëÉôʬ): ''e...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
plot "euler.dat" every ::line::line w p pt 6 ps 3
line=line+1
pause 0.2
if(line<144) reread
}}
&br;
3a) gnuplot (¥á¥Ë¥å¡¼ ¢ª Math ¢ª gnuplot) ¤òµ¯Æ°¤·¡¤
3b) ¾å¤Î¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë ''euler.dat'', gnuplot ¤ÎÆ°ºî¥Õ¥¡...
3c) gnuplot ¤ÎÌ¿Îá²èÌ̤Ç
load "euler.plt"
¤ÈÆþÎϤ¹¤ë¡¥ÌäÂ꤬¤Ê¤±¤ì¤Ð¡¤°Ê²¼¤Î¿Þ¤Î¤è¤¦¤Êɽ¼¨¤ÇÆ°²èŪ...
CENTER:&ref(./gnuplot-movie.png,60%);
&br;
// Ãí°Õ¥¢¥¤¥³¥ó
&ref(/materials/warning.png); gnuplot ¤Ç1¹Ô¤º¤Äɽ¼¨¤ò·«¤ê...
- ''reread'' : ¤³¤ì¤Ï¡¤¤½¤ÎÌ¿Î᤬Æþ¤Ã¤¿¥Õ¥¡¥¤¥ë¤òÆɤßľ¤¹...
- plot Ì¿Îá¤Î¸å¤í¤Ë¤Ä¤¤¤Æ¤¤¤ë ''every ::line::line'' : ¤³...
&br;
&ref(/materials/warning.png); ¤¹¤Ù¤Æ¤Î½Ö´Ö¤Î²èÁü¤òÍÑ°Õ¤·...
- ¥¦¥£¥ó¥É¥¦¥º¥à¡¼¥Ó¡¼¥á¡¼¥«¡¼
(Âç³Ø¤ÎPC ¤Î¾ì¹ç: ¥á¥Ë¥å¡¼ ¢ª ¥×¥í¥°¥é¥à ¢ª ¥¢¥¯¥»¥µ¥ê ¢ª ¥Õ...
- [[TMPGEnc ̵ÎÁÈÇ:http://www.tmpgenc.net/ja/j_download.h...
¤Ê¤É¤¬¡¤Unix ·Ï(´Þ¤à Mac)¤Ê¤é¤Ð
- ffmpeg
¤Ê¤É¤¬¤¢¤ë¤Î¤Ç(¼«Âð¤Ç¥¤¥ó¥¹¥È¡¼¥ë¤¬É¬Íפʤâ¤Î¤Ï¥¤¥ó¥¹¥È¡¼...
&br;
* º£Æü¤ÎÁí»Å¾å¤² [#d01db1cd]
¾å¤ÎÎãƱÍͤˡ¤º£Å٤ϽÅÎϲ¼¤Ç Newton ¤Î±¿Æ°ÊýÄø¼°¤Ë±è¤Ã¤Æ...
CENTER:&ref(./pendulum.png,60%);
¤Þ¤º¤Ï³Æ¾ò·ï¤ò°Ê²¼¤Î¤è¤¦¤Ë¤·¤Æ¤ß¤è¤¦¡¥
''[¾õ¶·¾ò·ï]''
¿¶¤ê»Ò¤Îɳ¤ÎŤµ L = 1.0 m
''[½é´ü¾ò·ï]''
½é´ü³ÑÅÙ θ(0) = π/3 (rad) = 60.0 (ÅÙ)
½é´ü®ÅÙ dθ/dt(0) = 0.0 (rad/s)
''[½ªÎ»¾ò·ï]''
t = 0 sec ¤«¤é³«»Ï¤·¤Æ¡¤³Æ¼«¼«Ê¬¤Ç·è¤á¤¿»þ´Ö t = T_limit ...
''[¶á»÷¾ò·ï]''
»þ´Ö¹ï¤ßÉý ¢¤t = 0.01 sec (¾¯¤·¾®¤µ¤¯¤·¤Æ¤ª¤¤¤¿)
''[¶á»÷ÊýË¡]''
Euler Ë¡
&br;
&ref(/materials/warning.png); º£Å٤϶õ´Ö¤¬Æ󼡸µ¤ÎÌäÂê¤À...
¤½¤³¤Ç¡¤¤Þ¤º¤Ï Newton ¤Î±¿Æ°ÊýÄø¼°¤ò³ÑÅÙ¤ËÂФ¹¤ë¾ïÈùʬÊý...
¤½¤ì¤«¤é¡¤¾å¤ÎÎã¤Î¤è¤¦¤Ë¡¤½¾Â°ÊÑ¿ô¤ò¿·¤¿¤Ë²Ã¤¨¤ë¤³¤È¤ÇÌä...
¤½¤¦¤¹¤ì¤Ð Euler Ë¡¤Ç¶á»÷Ū¤Ë²ò¤±¤ë¤À¤í¤¦¡¥
¤¢¤È¡¤¥×¥í¥°¥é¥à¤Î¥Ç¡¼¥¿½ÐÎÏ»þ¤Ë x, y ¤ÎÆ󼡸µ¤ÎºÂɸ¤ËÊÑ...
&br;
** ¾åµé¼Ô¸þ¤±(1) [#fc3e4a8a]
¡ÖÆó½Å¿¶¤ê»Ò¡×(°ì¤Ä¤á¤Î¿¶¤ê»Ò¤Ë¤µ¤é¤Ë¿¶¤ê»Ò¤¬¤Ö¤é²¼¤¬¤Ã¤Æ...
&br;
** ¾åµé¼Ô¸þ¤±(2) [#rbd96073]
Euler Ë¡¤Ç¤Ï¤Ê¤¯¡¤¸Åŵ Runge-Kutta Ë¡¤È¤è¤Ð¤ì¤ëÊýË¡¤Ë¤Ä¤¤...
&br;
* ¥ì¥Ý¡¼¥È [#v61f4984]
ËÜÆü¼õ¤±¤¿¹ÖµÁ¤ª¤è¤Ó¹Ô¤Ã¤¿¼Â½¬¤Ë¤Ä¤¤¤Æ¡¤´Êñ¤Ë¤Þ¤È¤á¤¿Êó...
¤Þ¤¿¡¤Áí»Å¾å¤²¤ÎÉôʬ¤Ç¼«Ê¬¤Ç½ñ¤¤¤¿¥×¥í¥°¥é¥à¤òÊó¹ð¤»¤è.
¤â¤Á¤í¤ó³Æ¼«¤Î
+ ½ê°(³ØÉô¡¤³Ø²Ê)
+ ³ØÀÒÈÖ¹æ
+ ³Øǯ
+ »á̾
+ Æü»þ
+ ´Î¿´¤Î¥ì¥Ý¡¼¥ÈÆâÍÆ(ÆÀ¤¿Ãθ«¡¤ºî¶È¤Ë¤Ä¤¤¤Æµ¤¤Å¤¤¤¿¤³¤ÈÅù...
¤ò½ñ¤¯¤Î¤ò˺¤ì¤Ê¤¤¤è¤¦¤Ë.
* about Icons, ClipArts [#d80975f6]
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¡×.
// ¥³¥Þ¥ó¥É¥é¥¤¥ó½ÐÎϤϡֹÔƬ¤ò > ¤Ç»Ï¤á¤ë¡×.
// ¼Â½¬¥¢¥¤¥³¥ó
// &ref(/materials/notes.png);
// Ãí°Õ¥¢¥¤¥³¥ó
// &ref(/materials/warning.png);
// Link ¥¢¥¤¥³¥ó
// &ref(/materials/JNorth_arrow-right-sm.png);
// OK ¥¢¥¤¥³¥ó
// &ref(/materials/OK.png);
// NG ¥¢¥¤¥³¥ó
// &ref(/materials/NG.png);
// Âçʸ»ú¤Ç¤Î¶¯Ä´
// 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 [#z81ce357]
Á°²ó¤ÎÁí»Å¾å¤²¤Ï¡¤Í¿¤¨¤é¤ì¤¿ÃÏ¿Þ¤ÎÆóÅÀ´Ö¤ÇºÇû·ÐÏ©¤òÆ»¤¬...
(ÃϿޤˤĤ¤¤Æ¤ÏÁ°²ó¤Î web ¤ò»²¾È¤Î¤³¤È)
¿Þ¤¬Èó¾ï¤ËÁÇľ¤Ç´Êñ¤Ê·Á¤ò¤·¤Æ¤¤¤ë¤Î¤Ç¡¤ºÇû·ÐÏ©¤Î¸Ä¿ô¤ò...
¶ñÂÎŪ¤Ë¤Ï¡¤
&br;
¡Ö¤¢¤ëÅÀ¤òÄ̤ëºÇû·ÐÏ©¤Ï¡¤¤½¤Î¾å¤ÎÅÀ¤«±¦¤ÎÅÀ¤òÄ̤äƤä¤Ã...
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¤Î¤Ç¡¤¤³¤ì¤Ï¸À¤¤´¹¤¨¤ë¤È¡¤
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¡Ö¤¢¤ëÅÀ¤òÄ̤ëºÇû·ÐÏ©¤Î¿ô = ¤½¤Î¾å¤ÎÅÀ¤òÄ̤ëºÇû·ÐÏ©¤Î...
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¤È¤¤¤¦¤³¤È¤Ë¤Ê¤ë¡¥¤¢¤È¤Ï¤³¤ì¤ò¶ñÂÎŪ¤Ë¤·¤Æ¤¤¤±¤Ð¤è¤¤¡¥
Î㤨¤ÐÃÏ¿Þ¤òÁÇľ¤Ë x,y ºÂɸ¤Ç°Ê²¼¤Î¤è¤¦¤ËÆÃħÉÕ¤±¤¿¤È¤·¤Æ¡¤
CENTER:&ref(./route-exp.png,70%);
¤Î¤è¤¦¤Ë¹Í¤¨¤¿¤È¤·¤è¤¦¡¥
¤³¤Î¤È¤¡¤ºÂɸ (i,j) (0 ≤ i ≤ 6, 0 ≤ j ≤ 4)¤Î...
CENTER:&ref(./map-eq-1.png);
¤È¤Ê¤ë¤Î¤Ç¡¤¤³¤ì¤ò»È¤¨¤Ð¤è¤¤¡¥¤¢¤È¤Ï¡¤¤³¤Î´Ø·¸¼°¤òÅú¤¨¤Ë...
¤Ê¤ª¡¤¾å¤Î¼°¤òÅÓÃæ¤Þ¤Ç¼ê¤ÇŸ³«¤·¤¿·Á¤Î
CENTER:&ref(./map-eq-2.png);
¤ò»È¤Ã¤Æ¤âÎɤ¤¡¥¤¿¤À¡¤¤³¤¦¤¤¤¦¤è¤¦¤Ë¡Ö¿Í´Ö¤¬ÅÓÃæ¤Þ¤Ç²ðÆþ...
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** ºÆµ¢ÄêµÁ¤ò»È¤¦¾ì¹ç [#q58a3e88]
¤³¤ì¤Ï¿ô¼°¤òÁÇľ¤Ë»È¤¨¤Ð¤è¤¤¤Î¤Ç¡¤Î㤨¤Ð°Ê²¼¤Î¤è¤¦¤Ë¤Ê¤ë...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# f ¤òµá¤á¤ëºÆµ¢ÄêµÁ¼°
def f(i,j)
if ((i==6) && (j==4)) then
return 1
elsif (j==4) then
return f(i+1,4)
elsif (i==6) then
return f(6,j+1)
else
return f(i+1,j) + f(i, j+1)
end
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# f(0,0) ¤ÎÃͤò½ÐÎϤ¹¤ë¡¥
print(f(0,0),"\n")
}}
&br;
** ưŪ·×²èË¡¤â¤É¤¤ò»È¤¦¾ì¹ç [#ge33c2ea]
±¦¾å¤Î Start ÃÏÅÀ¤«¤é¡¤¡Ö²¿¥¹¥Æ¥Ã¥×Ìܤ«¡×¤È¤¤¤¦¤³¤È¤ËÃåÌÜ...
CENTER:&ref(./route-exp-2.png,70%);
¾¯¤·¹©Éפ¬¤¤¤ë¤¬¡¤¤Þ¤¢Î㤨¤Ð¼¡¤Î¤è¤¦¤Ë¥×¥í¥°¥é¥à¤ò½ñ¤±¤ë...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
include Math
# step ¤Î¾®¤µ¤¤¤Û¤¦¤«¤é·×»»¤·¤Æ¤¤¤Ã¤Æ¡¤Goal ¤Ç¤ÎÃͤòÊÖ¤¹....
def calc_top(nx,ny)
# ³ÆÅÀ¤òÄ̤ëºÇû·ÐÏ©¿ô¤òµÏ¿¤·¤Æ¤ª¤¯ÇÛÎó¤òÍÑ°Õ¤·¤è¤¦¡¥
f = Array.new(nx+1){ Array.new(ny+1){ 0 } }
# Start ÃÏÅÀ¤Ç¤Î f ¤Ï 1 ¤À¤Í¡¥
f[nx][ny] = 1
# Áí¥¹¥Æ¥Ã¥×¿ô
all_step = nx + ny
# step 1 ¤«¤é all_step ¤Þ¤Ç
for step in 1..all_step do
# Ʊ¤¸ step ¤ÎÅÀ¤Ï x + y = all_step - step ¤òËþ¤¿¤¹...
for i in 0..(all_step - step) do
j = (all_step - step) - i
if ((0 <= i) && (i <= nx) && (0 <= j) && (j <= ny))...
# ¤¢¤È¤ÏÉáÄ̤˷׻»¤¹¤ë
if (i==nx) then
f[i][j] = f[i][j+1]
elsif (j==ny) then
f[i][j] = f[i+1][j]
else
f[i][j] = f[i+1][j] + f[i][j+1]
end
end
end
end
# f(0,0) ¤òÊÖ¤¹¡¥
return f[0][0]
end
# Goal ¤Ç¤Î f ¤ÎÃͤò·×»»¤¹¤ë
ans = calc_top(6,4)
# ÃΤꤿ¤¤Ãͤòɽ¼¨¤¹¤ë
print(ans,"\n")
}}
** ¾¯¤·¸¤¤¹Í¤¨Êý [#ec4aa7e8]
ºÇû·ÐÏ©¿ô¤Î°Í¸´Ø·¸¤ò¹Í¤¨¤ë¤È¡Ö±¦¾å¤«¤éº¸²¼¤Ë¼Ð¤á¡×¤ËÏÃ...
¸À¤¤´¹¤¨¤ë¤È¡¤¡Ö¤³¤Î¼Ð¤á¤ÎÊý¸þ¤¬ÁÇľ¤ÊÊý¸þ¡×¤Ë¤Ê¤ë¤Î¤Ç¡¤...
¼ÂºÝ¤Ë·¹¤±¤Æ¤ß¤è¤¦¡¥
¤¹¤ë¤È¡¤°Í¸´Ø·¸¤¬Á°²ó¤Î¡ÖÌÚ¹½Â¤¡×¤Î¤È¤³¤í¤Ç¤ä¤Ã¤¿ÏäÈÁ´...
¤½¤³¤Ç¡¤¤¿¤È¤¨¤ÐÁ´ÂΤ¬¡Ö¤ï¤«¤ê¤ä¤¹¤¤ÌÚ¹½Â¤¡×¤Ë¤Ê¤ë¤è¤¦¤Ë...
CENTER:&ref(./route-tree.png,60%);
¤¢¤È¤Ï¡¤²¼¤Î¿ô»ú¤ò¤¹¤È¼«Ê¬¤Î¿ô»ú¤Ë¤Ê¤ë¡¤¤È¤¤¤¦»ÅÁȤߤò...
¤³¤ì¤Ç¹Í¤¨¤ë¤È¡¤Æ°Åª·×²èË¡¤â¤É¤¤Î¥×¥í¥°¥é¥ß¥ó¥°¤â¾å¤È°ã...
·×»»Î̤ÏÁý¤¨¤ë¤¬¡¤¤³¤¦¤·¤¿ÁÇľ¤Ê¥×¥í¥°¥é¥à¤Ë¤Ï¥ß¥¹¤¬Æþ¤ë...
Åú¤¨¤¬´Ö°ã¤Ã¤Æ¤¤¤ì¤Ð°ÕÌ£¤¬Ìµ¤¤¤Î¤À¤«¤é¡¤¤Þ¤º¤Ï¤³¤¦¤·¤¿¡Ö...
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¤³¤Î¤è¤¦¤Ë¡¤
&br;
CENTER:&size(24){''°Í¸´Ø·¸¤Ê¤É¤ò¤è¤¯¹Í¤¨¤Æ¡¤''};
CENTER:&size(24){''»öÁ°¤ËÌäÂꤽ¤Î¤â¤Î¤ò½èÍý¤·¤ä¤¹¤¤·Á¤ËÍý...
CENTER:&size(24){''¥×¥í¥°¥é¥ß¥ó¥°¤Ë¤Ï½ÅÍפǤ¢¤ë¡¥''};
&br;
* Áí¹çÎÏ: ÈùʬÊýÄø¼°¤ò²ò¤¤¤Æ, ²ò¤ò¸«¤Æ¤ß¤è¤¦ [#u0bdf45e]
¤³¤ì¤Þ¤Ç¤Ç¥×¥í¥°¥é¥ß¥ó¥°¤Ë¤Ä¤¤¤Æ''ºÇÄã¸Â''¤ÎÃμ±¤Ï¿È¤Ë¤Ä...
¤¤¤í¤ó¤ÊÂêºà¤¬¤¢¤ë¤¬¡¤¤Þ¤º¤Ï¤´¤¯´Êñ¤Ê¾ïÈùʬÊýÄø¼°¤ËÂФ·...
&br;
** ¼«Í³Íî²¼¤ò¥·¥ß¥å¥ì¡¼¥È¤·¤Æ¤ß¤ë [#w4302938]
³ØÀ¸¤¬ºÇ¤â¤è¤¯ÃΤäƤ¤¤ë¾ïÈùʬÊýÄø¼°¤Ç¤¢¤ë¡¤Newton ÎϳؤË...
¤Þ¤º¤â¤Ã¤È¤â´Êñ¤Ê¡¤¡Ö¿¿¶õÃæ¤òʪÂΤ¬¼«Í³Íî²¼¤·¤Æ¤¯¤ëÍÍ»Ò...
»þ´Ö¤ò t sec, ÃϾ夫¤é¤ÎʪÂΤι⤵¤ò u(t) m¡¤½ÅÎϲîÅÙ g...
Newton ¤Î±¿Æ°ÊýÄø¼° F = ma ¤è¤ê¡¤
CENTER:&ref(./newton.png,70%);
CENTER:''ʪÂΤι⤵¤Ë¤Ä¤¤¤Æ¤Î¾ïÈùʬÊýÄø¼°''
¤È¤¤¤¦¾ïÈùʬÊýÄø¼°¤¬ÆÀ¤é¤ì¤ë¡¥
¤³¤ì¤ÏÆ󳬾ïÈùʬÊýÄø¼°¤Ç¾¯¤·°·¤¤¤Ë¤¯¤¤¤Î¤Ç¡¤Â®ÅÙ v = du/d...
CENTER:&ref(./newton-2.png,70%);
CENTER:''ʪÂΤι⤵¤Ë¤Ä¤¤¤Æ¤Î¾ïÈùʬÊýÄø¼°(ÊÑ·ÁÈÇ)''
¤È¤¤¤¦¤â¤Î¤ËÊÑ·Á¤·¤Æ¡¤¤³¤ì¤Ë¤Ä¤¤¤Æ¹Í¤¨¤è¤¦¡¥
¤³¤ÎÊýÄø¼°¤Ï¼ê¤Ç²ò¤±¤Æ¤·¤Þ¤¦¤¬¡¤¼ê¤Ç¸·Ì©²ò¤¬µá¤Þ¤é¤Ê¤¤¾ì...
&br;
*** Euler Ë¡ [#q2524109]
Euler Ë¡¤È¤¤¤¦¤Î¤Ï´Êñ¤Ç¡¤»þ´ÖȯŸ¹à¤òÁ°¿Êº¹Ê¬¤Ç¶á»÷¤¹¤ë...
¤Þ¤¢¡¤ÍýÏÀ¤ò¸À¤¦¤è¤ê¸«¤¿¤Û¤¦¤¬Áᤤ¤À¤í¤¦¡¥
º£²ó¤Î¾ì¹ç¡¤»þ´ÖÊÑ¿ô t ¤ò ¢¤t ¤ÎÉý¤Ç¡Ö¹ï¤à¡×¤³¤È¤Ë¤·¤Æ¡¤¾å...
CENTER:&ref(./euler.png,70%);
CENTER:''¾å¤Î¾ïÈùʬÊýÄø¼°¤ò Euler Ë¡¤Ç¡Ö¶á»÷¡×¤·¤¿¤â¤Î''
¤È¤¹¤ë¤Î¤¬ Euler Ë¡¤Ç¤¢¤ë¡¥¤½¤·¤Æ¤³¤Î¼°¤ò¤¤ì¤¤¤Ë½ñ¤Ä¾¤¹...
CENTER:&ref(./euler-2.png,70%);
CENTER:''¾å¤Î¾ïÈùʬÊýÄø¼°¤ò Euler Ë¡¤Ç¡Ö¶á»÷¡×¤·¤¿¤â¤Î(º¸...
¤È¤Ê¤ë¤Î¤Ç¡¤¤³¤ì¤ò¤ß¤ë¤È¡Ö±¦ÊÕ¤ËÃΤäƤ¤¤ëÃͤòÂåÆþ¤¹¤ë¤À...
¾ïÈùʬÊýÄø¼°¤ò¤³¤Î¤è¤¦¤Ë¶á»÷¼°¤ËÃÖ¤´¹¤¨¤ë¤Î¤¬ Euler Ë¡¤Ç...
¤³¤ì¤Ê¤é¥×¥í¥°¥é¥à¤¬½ñ¤±¤½¤¦¤À¤È¤¤¤¦´¶¿¨¤¬ÆÀ¤é¤ì¤ë¤À¤í¤¦¡¥
&br;
&ref(/materials/warning.png); ¤â¤Á¤í¤ó¡¤Euler Ë¡¤Çºî¤Ã¤¿...
&br;
*** ÌäÂêÀßÄê [#o50d4c8e]
¤µ¤Æ¡¤¥·¥ß¥å¥ì¡¼¥È¤¹¤ë¤Ë¤Ï¶ñÂÎŪ¤Ê¾ò·ï¤òµÍ¤á¤Ê¤¤¤È¤¤¤±¤Ê...
¤½¤³¤Ç¡¤°Ê²¼¤Î¤è¤¦¤Ë½é´ü¾ò·ï¤Ê¤É¤òÀßÄꤷ¤è¤¦¡¥
''[½é´ü¾ò·ï]''
½é´ü¹â¤µ u(0) = 1000.0 (m)
½é´ü®ÅÙ v(0) = 0.0 (m/s)
''[½ªÎ»¾ò·ï]''
¹â¤µ¤¬ 0 m°Ê²¼¤È¤Ê¤Ã¤¿¤é¥·¥ß¥å¥ì¡¼¥·¥ç¥ó½ªÎ».
''[¶á»÷¾ò·ï]''
»þ´Ö¹ï¤ßÉý ¢¤t = 0.1 sec
&br;
*** ¥×¥í¥°¥é¥à [#d15c251c]
// ¼Â½¬¥¢¥¤¥³¥ó
&ref(/materials/notes.png); °Ê²¼¤ÎÉôʬ¤Ï¼Â½¬¤·¤Ê¤¬¤éÍý²ò...
&br;
¥×¥í¥°¥é¥à¤Ï¾å¤Î¾ò·ï¤Ë½¾¤Ã¤Æ·×»»¤·¤Æ »þ´Ö, ¹â¤µ ¤Î¿ô»ú¥Ú...
¤¹¤ë¤È¡¤¤À¤¤¤¿¤¤°Ê²¼¤Î¤è¤¦¤Ê´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¤«¡¥
// 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)
g = 9.8
u_new = u + v*dt
v_new = v - g*dt
return u_new, v_new
end
# »þ´Ö¤È¹â¤µ¤ò½ÐÎϤ¹¤ë
def output(u, time)
print(time,", ",u,"\n")
end
# °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ
# ½é´üÃÍ
u = 1000.0
v = 0.0
time = 0.0
# »þ´Ö¹ï¤ßÉý
dt = 0.1
# ¹â¤µ u ¤¬Àµ¤Î¤¦¤Á¤Ï·×»»¤ò·«¤êÊÖ¤¹
while (u > 0) do
# ¹â¤µ¤È»þ´Ö¤ò½ÐÎÏ
output(u, time)
# Euler Ë¡¤Ç¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë
u,v = euler(u,v,dt)
# »þ´Ö¤ò¹¹¿·
time += dt
end
}}
&br;
*** ¥×¥í¥°¥é¥à¤òÆ°¤«¤·¤Æ¥Ç¡¼¥¿¤òÆÀ¤ë [#r786047b]
¾å¤Î¥×¥í¥°¥é¥à¤ò¼Â¹Ô¤·¤Æ¡¤¥Ç¡¼¥¿¤òÆÀ¤è¤¦¡¥ÆÀ¤é¤ì¤¿¥Ç¡¼¥¿...
¤½¤ì¤Ë¤ÏÎ㤨¤Ð¡¤¾å¤Î¥×¥í¥°¥é¥à¥Õ¥¡¥¤¥ë̾¤¬ euler.rb ¤À¤È...
ruby -w euler.rb > euler.dat
¤Ê¤É¤È¤·¤Æ¼Â¹Ô¤¹¤ì¤Ð¤è¤¤¡Ä¤Î¤Ï³Ð¤¨¤Æ¤¤¤ë¤Í¡© ¤³¤Î¾ì¹ç¡¤¥Ç...
&br;
*** ÆÀ¤é¤ì¤¿¥Ç¡¼¥¿¤òÆ°²èŪ¤Ë¸«¤Æ¤ß¤è¤¦ [#h76da810]
¾å¤Î¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë¤ò¸«¤Æ¤ß¤ë¤È¡¤Á´Éô¤Ç 144¹Ô¤¢¤ë¡¥¤½¤³¤Ç...
¤½¤³¤Ç¡¤°Ê²¼¤Î¤è¤¦¤Ëºî¶È¤·¤Æ¤ß¤è¤¦¡¥
&br;
1) gnuplot ¤ÎÆ°ºî¥Õ¥¡¥¤¥ë¤òºî¤ë: ''euler.plt'' ¤È¤¤¤¦Ì¾...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
set xrange[0:15]
set yrange[0:1000]
set xlabel "Time"
set ylabel "Height"
unset key
line=0
load "euler.loop"
}}
&br;
2) gnuplot ¤ÎÆ°ºî¥Õ¥¡¥¤¥ë¤òºî¤ë(1¹Ô¤º¤Äɽ¼¨¤¹¤ëÉôʬ): ''e...
// programu source ɽµ
#highlighter(language=ruby,number=on,cache=on){{
plot "euler.dat" every ::line::line w p pt 6 ps 3
line=line+1
pause 0.2
if(line<144) reread
}}
&br;
3a) gnuplot (¥á¥Ë¥å¡¼ ¢ª Math ¢ª gnuplot) ¤òµ¯Æ°¤·¡¤
3b) ¾å¤Î¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë ''euler.dat'', gnuplot ¤ÎÆ°ºî¥Õ¥¡...
3c) gnuplot ¤ÎÌ¿Îá²èÌ̤Ç
load "euler.plt"
¤ÈÆþÎϤ¹¤ë¡¥ÌäÂ꤬¤Ê¤±¤ì¤Ð¡¤°Ê²¼¤Î¿Þ¤Î¤è¤¦¤Êɽ¼¨¤ÇÆ°²èŪ...
CENTER:&ref(./gnuplot-movie.png,60%);
&br;
// Ãí°Õ¥¢¥¤¥³¥ó
&ref(/materials/warning.png); gnuplot ¤Ç1¹Ô¤º¤Äɽ¼¨¤ò·«¤ê...
- ''reread'' : ¤³¤ì¤Ï¡¤¤½¤ÎÌ¿Î᤬Æþ¤Ã¤¿¥Õ¥¡¥¤¥ë¤òÆɤßľ¤¹...
- plot Ì¿Îá¤Î¸å¤í¤Ë¤Ä¤¤¤Æ¤¤¤ë ''every ::line::line'' : ¤³...
&br;
&ref(/materials/warning.png); ¤¹¤Ù¤Æ¤Î½Ö´Ö¤Î²èÁü¤òÍÑ°Õ¤·...
- ¥¦¥£¥ó¥É¥¦¥º¥à¡¼¥Ó¡¼¥á¡¼¥«¡¼
(Âç³Ø¤ÎPC ¤Î¾ì¹ç: ¥á¥Ë¥å¡¼ ¢ª ¥×¥í¥°¥é¥à ¢ª ¥¢¥¯¥»¥µ¥ê ¢ª ¥Õ...
- [[TMPGEnc ̵ÎÁÈÇ:http://www.tmpgenc.net/ja/j_download.h...
¤Ê¤É¤¬¡¤Unix ·Ï(´Þ¤à Mac)¤Ê¤é¤Ð
- ffmpeg
¤Ê¤É¤¬¤¢¤ë¤Î¤Ç(¼«Âð¤Ç¥¤¥ó¥¹¥È¡¼¥ë¤¬É¬Íפʤâ¤Î¤Ï¥¤¥ó¥¹¥È¡¼...
&br;
* º£Æü¤ÎÁí»Å¾å¤² [#d01db1cd]
¾å¤ÎÎãƱÍͤˡ¤º£Å٤ϽÅÎϲ¼¤Ç Newton ¤Î±¿Æ°ÊýÄø¼°¤Ë±è¤Ã¤Æ...
CENTER:&ref(./pendulum.png,60%);
¤Þ¤º¤Ï³Æ¾ò·ï¤ò°Ê²¼¤Î¤è¤¦¤Ë¤·¤Æ¤ß¤è¤¦¡¥
''[¾õ¶·¾ò·ï]''
¿¶¤ê»Ò¤Îɳ¤ÎŤµ L = 1.0 m
''[½é´ü¾ò·ï]''
½é´ü³ÑÅÙ θ(0) = π/3 (rad) = 60.0 (ÅÙ)
½é´ü®ÅÙ dθ/dt(0) = 0.0 (rad/s)
''[½ªÎ»¾ò·ï]''
t = 0 sec ¤«¤é³«»Ï¤·¤Æ¡¤³Æ¼«¼«Ê¬¤Ç·è¤á¤¿»þ´Ö t = T_limit ...
''[¶á»÷¾ò·ï]''
»þ´Ö¹ï¤ßÉý ¢¤t = 0.01 sec (¾¯¤·¾®¤µ¤¯¤·¤Æ¤ª¤¤¤¿)
''[¶á»÷ÊýË¡]''
Euler Ë¡
&br;
&ref(/materials/warning.png); º£Å٤϶õ´Ö¤¬Æ󼡸µ¤ÎÌäÂê¤À...
¤½¤³¤Ç¡¤¤Þ¤º¤Ï Newton ¤Î±¿Æ°ÊýÄø¼°¤ò³ÑÅÙ¤ËÂФ¹¤ë¾ïÈùʬÊý...
¤½¤ì¤«¤é¡¤¾å¤ÎÎã¤Î¤è¤¦¤Ë¡¤½¾Â°ÊÑ¿ô¤ò¿·¤¿¤Ë²Ã¤¨¤ë¤³¤È¤ÇÌä...
¤½¤¦¤¹¤ì¤Ð Euler Ë¡¤Ç¶á»÷Ū¤Ë²ò¤±¤ë¤À¤í¤¦¡¥
¤¢¤È¡¤¥×¥í¥°¥é¥à¤Î¥Ç¡¼¥¿½ÐÎÏ»þ¤Ë x, y ¤ÎÆ󼡸µ¤ÎºÂɸ¤ËÊÑ...
&br;
** ¾åµé¼Ô¸þ¤±(1) [#fc3e4a8a]
¡ÖÆó½Å¿¶¤ê»Ò¡×(°ì¤Ä¤á¤Î¿¶¤ê»Ò¤Ë¤µ¤é¤Ë¿¶¤ê»Ò¤¬¤Ö¤é²¼¤¬¤Ã¤Æ...
&br;
** ¾åµé¼Ô¸þ¤±(2) [#rbd96073]
Euler Ë¡¤Ç¤Ï¤Ê¤¯¡¤¸Åŵ Runge-Kutta Ë¡¤È¤è¤Ð¤ì¤ëÊýË¡¤Ë¤Ä¤¤...
&br;
* ¥ì¥Ý¡¼¥È [#v61f4984]
ËÜÆü¼õ¤±¤¿¹ÖµÁ¤ª¤è¤Ó¹Ô¤Ã¤¿¼Â½¬¤Ë¤Ä¤¤¤Æ¡¤´Êñ¤Ë¤Þ¤È¤á¤¿Êó...
¤Þ¤¿¡¤Áí»Å¾å¤²¤ÎÉôʬ¤Ç¼«Ê¬¤Ç½ñ¤¤¤¿¥×¥í¥°¥é¥à¤òÊó¹ð¤»¤è.
¤â¤Á¤í¤ó³Æ¼«¤Î
+ ½ê°(³ØÉô¡¤³Ø²Ê)
+ ³ØÀÒÈÖ¹æ
+ ³Øǯ
+ »á̾
+ Æü»þ
+ ´Î¿´¤Î¥ì¥Ý¡¼¥ÈÆâÍÆ(ÆÀ¤¿Ãθ«¡¤ºî¶È¤Ë¤Ä¤¤¤Æµ¤¤Å¤¤¤¿¤³¤ÈÅù...
¤ò½ñ¤¯¤Î¤ò˺¤ì¤Ê¤¤¤è¤¦¤Ë.
* about Icons, ClipArts [#d80975f6]
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¡×.
// ¥³¥Þ¥ó¥É¥é¥¤¥ó½ÐÎϤϡֹÔƬ¤ò > ¤Ç»Ï¤á¤ë¡×.
// ¼Â½¬¥¢¥¤¥³¥ó
// &ref(/materials/notes.png);
// Ãí°Õ¥¢¥¤¥³¥ó
// &ref(/materials/warning.png);
// Link ¥¢¥¤¥³¥ó
// &ref(/materials/JNorth_arrow-right-sm.png);
// OK ¥¢¥¤¥³¥ó
// &ref(/materials/OK.png);
// NG ¥¢¥¤¥³¥ó
// &ref(/materials/NG.png);
// Âçʸ»ú¤Ç¤Î¶¯Ä´
// CENTER:&size(24){''¤Û¤²¤Û¤²''};
// programu source ɽµ
// #highlighter(language=ruby,number=on,cache=on){{}}
¥Ú¡¼¥¸Ì¾: