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解微分方程+2分法解二元方程组

Posted by tasty at 2013-05-14 11:55:09 on Problem 3933 and last updated at 2013-05-14 11:58:20
先通过解微分方程算出平行于 斜面方向的速度和时间的函数关系  and垂直于斜面方向的速度和时间的函数关系,再对速度求积分,算出斜面方向的位移和时间的函数关系 and垂直于斜面方向的位移和时间的函数关系,再令垂直于斜面方向的位移为0,平行于斜面的位移的导数为0,得到两个关于初始速度的倾斜角theta和时间t的二元方程组:

   e^(-T)*(v0*f+g*sin(theta))==g*sin(theta)
  (v0*f*sin(theta-alpha)+g*cos(alpha))*(1-e^(-T))==g*T*cos(alpha)
其中v0为初速度,alpha为斜面倾斜角,T==f*t.这个方程组有两个解,
然后令h(theta)==(v0*f*sin(theta-alpha)+g*cos(alpha))*(1-e^(-T))-g*T*cos(alpha). 可以用二分枚举theta,用第一个公式解出T,判定h(mid)*h(high)的符号来 解出theta

复杂度为 log(精度)

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