求双曲螺旋线r={acosht，asinht，at}从t＝0起到t＝T的弧长I(T). I(T)=∫{0→T}√[(acosht)'^2+(asinht)'^2+(at)'^2]dt= =a∫{0→T}√[(sinht)^2+(cosht)^2+1]dt= =a∫{0→T}√[2(cosht)^2]dt= =a√2∫{0→T}coshtdt=a√2sinhT.
求双曲螺旋线r={acosht，asinht，at}从t＝0起到t＝T的弧长I(T). I(T)=∫{0→T}√[(acosht)'^2+(asinht)'^2+(at)'^2]dt= =a∫{0→T}√[(sinht)^2+(cosht)^2+1]dt= =a∫{0→T}√[2(cosht)^2]dt= =a√2∫{0→T}coshtdt=a√2sinhT.
