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¤Þ¤º¡¤±ôľ²¼Êý¸þ¤«¤é¤Î³ÑÅÙ¤ò θ rad ¤È¤¹¤ë¤È Newton ¤Î±¿Æ°ÊýÄø¼°¤¬

pendulum-eq.png
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¤Ëµ¢Ã夹¤ë¤Î¤Ï¹â¹»¤ÎʪÍý¤Î¼ø¶È¤Ç¤ä¤Ã¤Æ¤¤¤ë¤Ï¤º¤À(¿Í¤Ë¤è¤Ã¤Æ¤ÏÃæ³ØÀ¸¤Ç³Ø¤ó¤Ç¤¤¤ë¤Í)¡¥¤³¤ì¤â²ò¤¬¤ï¤«¤Ã¤Æ¤·¤Þ¤¦¤¬*1¡¤¥×¥í¥°¥é¥à¤Ç¶á»÷²ò¤òµá¤á¤è¤È¤¤¤¦ÌäÂê¤Ê¤Î¤Ç¤½¤Î¤è¤¦¤Ë¤·¤è¤¦¡¥
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pendulum-eq-mod.png
¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°(ÊÑ·ÁÈÇ)

¤È¤¤¤¦´¶¤¸¤Ë¤Ê¤ë¤À¤í¤¦¡¥¤½¤·¤Æ¡¤¾å¤ÎÊýÄø¼°¤ËÂФ·¤Æ Euler Ë¡¤òŬÍѤ¹¤ë¤È¡¤

pendulum-euler.png
¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°(ÊÑ·ÁÈǤΠEuler Ë¡¤Ë¤è¤ë¶á»÷)

¤È¤¤¤¦¶á»÷¼°¤¬ÆÀ¤é¤ì¤ë¡¥¤µ¤é¤Ë¤³¤ì¤ò°·¤¤¤ä¤¹¤¯Ä¾¤·¤Æ¡¤

pendulum-euler-mod.png
¿¶¤ê»Ò¤Î±¿Æ°ÊýÄø¼°(ÊÑ·ÁÈǤΠEuler Ë¡¤Ë¤è¤ë¶á»÷¤ò¤ï¤«¤ê¤ä¤¹¤¯¤·¤¿¤â¤Î)

¤È¤Ç¤­¤ë¤Î¤Ç¡¤¤³¤ì¤ò¤â¤È¤Ë¥×¥í¥°¥é¥à¤òÁȤ⤦¡¥ÍÍ¡¹¤Ê¶ñÂÎŪ¾ò·ï¤â¹þ¤ß¤Ç¡¤Á°²ó¤ÎÎãÂê¤Î¥×¥í¥°¥é¥à¤È¤Û¤È¤ó¤ÉÊѤï¤é¤Ê¤¤·Á¤Ç¡¤¤¿¤È¤¨¤Ð¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¤À¤í¤¦¡¥

  1. include Math

  2.  

  3. # Euler Ë¡¤Ë´ð¤Å¤¤¤Æ¡¤¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë

  4. def euler(u,v,dt,l)

  5.   g = 9.8

  6.  

  7.   u_new = u + v*dt

  8.   v_new = v - (g/l)*sin(u)*dt

  9.  

  10.   return u_new, v_new

  11. end

  12.  

  13. # x, y¤ò½ÐÎϤ¹¤ë

  14. def outputXY(u,l)

  15.   x = l*sin(u)

  16.   y = - l*cos(u)

  17.   print(x,", ",y,"\n")

  18. end

  19.  

  20. # °Ê²¼¡¤¥×¥í¥°¥é¥àËÜÂÎ

  21.  

  22. # ÌäÂê¾ò·ï

  23. l = 1.0

  24.  

  25. # ½é´üÃÍ

  26. u = PI/3.0

  27. v = 0.0

  28. time = 0.0

  29.  

  30. # ½ªÎ»»þ´Ö

  31. t_limit = 5.0

  32.  

  33. # »þ´Ö¹ï¤ßÉý

  34. dt = 0.01

  35.  

  36. # ½ªÎ»»þ´Ö¤Þ¤Ç¤Ï·×»»¤ò·«¤êÊÖ¤¹

  37. while (time < t_limit) do

  38.  

  39.   # x, y ¤ò½ÐÎÏ

  40.   outputXY(u,l)

  41.  

  42.   # Euler Ë¡¤Ç¼¡¤Î»þ´Ö¥¹¥Æ¥Ã¥×¤Î u,v ¤ò·×»»¤¹¤ë

  43.   u,v = euler(u,v,dt,l)

  44.  

  45.   # »þ´Ö¤ò¹¹¿·

  46.   time += dt

  47. end

Î㤨¤Ð¤³¤Î¥×¥í¥°¥é¥à¤òÆ°¤«¤»¤Ð¡¤Á´Éô¤Ç 501 ¹Ô¤È¤Ê¤ë¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë¤¬½ÐÍè¾å¤¬¤ë¡¥¤½¤³¤Ç¡¤¤½¤Î¥Ç¡¼¥¿¥Õ¥¡¥¤¥ë̾¤¬Î㤨¤Ð pendulum.dat ¤À¤È¤·¤Æ¡¤¤³¤ì¤òÆ°²èŪ¤Ëɽ¼¨¤¹¤ë¤¿¤á¤Î gnuplot ¤ÎÀßÄê¥Õ¥¡¥¤¥ë¤òÍÑ°Õ¤¹¤ë¡¥
¤Þ¤º¤ÏÀßÄê¥Õ¥¡¥¤¥ëËÜÂΤò pendulum.plt ¤È¤·¤Æ

  1. set xrange[-1.0:1.0]

  2. set yrange[-1.0:0.0]

  3. set xlabel "x"

  4. set ylabel "y"

  5. unset key

  6.  

  7. line=0

  8. load "pendulum.loop"

¤ÈÍÑ°Õ¤·¡¤¤µ¤é¤Ë1¹Ô¤º¤Ä¥°¥é¥Õ¤ò½ñ¤¯Éôʬ¤Î¤¿¤á¤Î¥Õ¥¡¥¤¥ë pendulum.loop ¤ò°Ê²¼¤Î¤è¤¦¤ËÍÑ°Õ¤·¤è¤¦¡¥

  1. plot "pendulum.dat" every ::line::line w p pt 6 ps 3

  2. line=line+1

  3. pause 0.01

  4. 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¤ò²èÌ̤Ǹ«¤ë¤³¤È¤¬¤Ç¤­¤ë¤Ï¤º¤À¡¥

warning.png 1¹Ô¤º¤Ä¤Î¥°¥é¥Õ¤ò²èÁü¥Õ¥¡¥¤¥ë¤Ë¤·¤Æ¤½¤ì¤ò¤â¤È¤ËÆ°²è¤òºî¤ë¾ì¹ç¤Ï¡¤Î㤨¤Ð pendulum.plt ¤ò

  1. set xrange[-1.0:1.0]

  2. set yrange[-1.0:0.0]

  3. set xlabel "x"

  4. set ylabel "y"

  5. unset key

  6.  

  7. set terminal png font arial 18 size 800,600

  8.  

  9. line=0

  10. load "pendulum.loop"

  11.  

  12. set terminal win

  13. set output

¤È¤·¡¤¥ë¡¼¥×Éôʬ¤ÎÀßÄê¥Õ¥¡¥¤¥ë pendulum.loop ¤ò

  1. op = sprintf("p-%03d.png",line)

  2. set output op

  3. plot "pendulum.dat" every ::line::line w p pt 6 ps 3

  4. line=line+1

  5. if(line<501) reread

¤Ê¤É¤È¤¹¤ì¤Ð¡¤gnuplot ¤Ç

 load "pendulum.plt"

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