20/11/28 20:55:35.00 FagdS+YP.net
>>601
0<a≦1 とする。
対数余弦函数を
y = {log(cos(k'x)) - log(cos(k'a))}/k',
(k' は等面積条件で決める。)
とすれば
y '= - tan(k'x)
L(a) = ∫[0,a] √{1+(y')^2} dx
= ∫[0,a] 1/cos(k'x) dx
= {log[1+sin(k'a)] - log[1-sin(k'a)]}/(2k'),
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a 放物線 cosh log(cos) 円弧(+線分)
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0.0 0.75 0.53 0.50 0.50
0.1 0.76301 0.667650 0.58835 0.57854 + 1.70%
0.2 0.79280 0.730424 0.67351 0.65708 + 2.50%
0.3 0.83423 0.791905 0.75300 0.73562 + 2.36%
0.4 0.88459 0.855342 0.82888 0.81416 + 1.81%
0.5 0.94211 0.921616 0.90352 0.89270 + 1.21%
0.6 1.00544 0.990922 0.97844 0.97124 + 0.74%
2/π 1.02989 1.017050 1.00613 1.00 + 0.61%
0.7 1.07359 1.063184 1.05449 1.04982 + 0.44%
0.8 1.14574 1.138208 1.13208 1.12899 + 0.27%
0.9 1.22127 1.215752 1.21138 1.20928 + 0.17%
1.0 1.29964 1.295561 1.29240 1.29095 + 0.11%
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