»°ËÞ½I—¹‚Ì‚¨’m‚点
‘ȉ~‘Ì
¥l‹C‹LŽ–×ݷݸÞ
øêŠT—v
‘ȉ~‘́i‚¾‚¦‚ñ‚½‚¢¤ellipsoidj‚Ƃ͑ȉ~‚ðŽOŽŸŒ³‚ÖŠg’£‚µ‚½‚悤‚Ȑ}Œ`‚Å‚ ‚褂»‚Ì•\–Ê‚Í“ñŽŸ‹È–Ê‚Å‚ ‚顑ȉ~–Ê‚Ì•û’öŽ®‚Í
x 2 a 2 + y 2 b 2 + z 2 c 2 = 1 {\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}+{\frac {z^{2}}{c^{2}}}=1} ‚Å‚ ‚é¡‚±‚±‚Å a, b, c ‚Í‚»‚ꂼ‚êxŽ²¤yŽ²¤zŽ²•ûŒü‚ÌŒa‚Ì”¼•ª‚Ì’·‚³‚É‘Š“–‚·‚é¡‚È‚¨ a = b = c ‚Å‚ ‚é‘ȉ~‘Ì‚Í‹…‚Å‚ ‚é¡‚Ü‚½ a, b, c ‚Ì‚¤‚¿‚¢‚¸‚ê‚©2‚‚ª“™‚µ‚¢‘ȉ~‘̂͑ȉ~‚ÌŽ²‚𒆐S‚ɑȉ~‚ð‰ñ“]‚µ‚Ä“¾‚ç‚ê‚é‰ñ“]‘Ì‚Å‚ ‚褒·Ž²‚ð‰ñ“]Ž²‚É‚µ‚½‚à‚Ì‚ð’·‹…¤’ZŽ²‚ð‰ñ“]Ž²‚É‚µ‚½‚à‚Ì‚ðG‹…‚Æ‚¢‚¢¤•¹‚¹‚ĉñ“]‘ȉ~‘̂ƌĂ΂ê‚顑ȉ~‘Ì‚Í‹…‚Æ“¯—l‚Éxy•½–ʤyz•½–ʤzx•½–Ê‚ÉŠÖ‚µ‚đΏ̂ł ‚é¡

‘ȉ~‘̂̐«Ž¿‚ð•\‚·Ž®[•ÒW]

‘ȉ~–Ê‚Ì”}‰î•Ï”•\Ž¦‚͋ɍÀ•WŒn‚ð—p‚¢‚é‚Æ

x = a sin θ cos φ y = b sin θ sin φ z = c cos θ {\displaystyle {\begin{aligned}x&=a\sin \theta \cos \varphi \\y&=b\sin \theta \sin \varphi \\z&=c\cos \theta \end{aligned}}} 0 θ π , 0 φ 2 π {\displaystyle 0\leq \theta \leq \pi ,\quad 0\leq \varphi \leq 2\pi } ‚Æ•\‚³‚ê‚顑ȉ~‘Ì‚Ì‘ÌÏ V ‚Í

V = 4 3 π a b c {\displaystyle V={\frac {4}{3}}\pi abc} ‚Å‚ ‚é¡•\–ÊÏ S ‚Í

S = 2 π ( c 2 + b a 2 c 2 E ( o ε , m ) + b c 2 a 2 c 2 F ( o ε , m ) ) {\displaystyle S=2\pi \left(c^{2}+b{\sqrt {a^{2}-c^{2}}}E(o\!\varepsilon ,m)+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(o\!\varepsilon ,m)\right)} ‚Æ‚È‚é¡‚ÍÓ¼Þ­×°Šp¤¤¤ ‚Í‚»‚ꂼ‚ê‘æˆêŽí‚¨‚æ‚Ñ‘æ“ñŽí‘ȉ~Ï•ª‚Å‚ ‚顋ߎ—Ž®‚Å

S 4 π ( a p b p + a p c p + b p c p 3 ) 1 / p {\displaystyle S\approx 4\pi \!\left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}} ‚Æ‚¢‚¤ŒöŽ®‚ª’m‚ç‚ê‚Ä‚¢‚é¡‚±‚±‚Åp‚͒萔‚Ťp = 1.6075 ‚Ì‚Æ‚«Œë·‚͍őå‚Å‚à1.061%‚Å‚ ‚é¡

ŠÖ˜A€–Ú[•ÒW]

‘ȉ~
‘ȉ~Ï•ª
‘o‹È–Ê
o“T:Wikipedia
2018/11/15 18:01
ù¿l‹C‹LŽ–×ݷݸÞ
2020/02/17 XV
 1ˆÊ¨“ú–{
 2ˆÊª•’J—F
 3ˆÊ«ê Œ´Œh”V
 4ˆÊ¨‰ªè”ü—
 5ˆÊ¨–쑺¹’m‘ã
£ã‚É–ß‚é
[9]WikipediaįÌß
[0]gooįÌß
¡–Ɛӎ–€
(C)NTT Resonant