ケルヴィン男爵さんの積分器は掛け算割り算ばかりでなく積分計算もできます。すごいですね。
図に従って説明します。
水平円盤の回転中心から垂直円盤との接触点までの距離をUとします。
垂直円盤の半径はRとします。
水平円盤の回転角をΘとします。
垂直円盤の回転角をΘ’(シータダッシュ)とします。
∫長さ×dt=回転角度
水平円盤の回転角ΔΘに対する垂直円盤の回転角ΔΘ’(シータダッシュ)は
ΔΘ’(シータダッシュ)=(U/R)ΔΘ
Uは時間tの関数であり円盤の角速度ωとすると
ΔΘ=ωΔt
Θ’=(ω/R)×R(t)dt
Θ(t)=∫U(t)dtの積分計算ができます。
二階積分を行うときは垂直円盤を連結して実現します。
二段目の垂直円盤の回転角をΘ2’とします。
二段目の水平円盤の回転角速度をΘ2とします。
二段目の垂直円盤の半径をR2とします。
Θ2’=ω1ω2U2/R2×∫[∫R1(t)dt]dt
となって二階積分 ∫∫U(t)dt という二階積分ができます。
今回までのケルヴィン男爵さんの積分器は垂直円盤の軸が水平円盤の動径に平行の場合でした。(垂直円盤の軸をわざとずらした角度をつけるタイプのものもあります。)
ケルヴィン男爵さんの積分器で積分計算ができる


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