%20设定参数%0AW%20%3D%201%3B%0AV%20%3D%203%3B%0AX1f%20%3D%2010%3B%0AX2f%20%3D%2020%3B%0A%0Asyms%20H%20lmd1%20lmd2%20x1%20x2%20u%0A%0A%2F%2F%20写出系统的哈密顿函数%0AH%20%3D%20-1%20%2B%20lmd1%20*%20V%20*%20cos(u)%20%2B%20lmd1%20*%20W%20%2B%20lmd2%20*%20V%20*%20sin(u)%3B%0A%0ADlmd1%20%3D%20-diff(H,%20x1)%3B%0ADlmd2%20%3D%20-diff(H,%20x2)%3B%0A%0AU%20%3D%20solve(diff(H,%20u))%3B%0A%0A%2F%2F%20u为指数形式,较复杂,可将其化简为u%3Darctan(lmd2%2Flmd1)%3B%0A[lmd1,%20lmd2]%20%3D%20dsolve(Dlmd1%20%3D%3D%200,%20Dlmd2%20%3D%3D%200)%3B%0A%0A%2F%2F解得%20lmd1%3Da,lmd2%3Db,令b%2Fa%3Dc%0A[x1,%20x2]%20%3D%20dsolve(diff(x1)%20%3D%3D%203%20*%20cos(atan(lmd2%20/%20lmd1))%20%2B%201,%20diff(x2)%20%3D%3D%203%20*%20sin(atan(lmd2%20/%20lmd1)))%3B%0A%0A%2F%2F为书写方便,将x1,x2的常数项分别记为d,e,%20t0是出发时间,t1是到达时间%0A[c,%20d,%20e,%20t0,%20t1]%20%3D%20solve(d%20%2B%20t0%20*%20(1%20%2B%203%20/%20(c^2%20%2B%201)^(1/2))%20%3D%3D%200,%20d%20%2B%20t1%20*%20(1%20%2B%203%20/%20(c^2%20%2B%201)^(1/2))%20%3D%3D%2010,%20e%20%2B%20(3%20*%20c%20*%20t0)%20/%20((c^2%20%2B%201)^(1/2))%20%3D%3D%200,%20e%20%2B%20(3%20*%20c%20*%20t1)%20/%20(c^2%20%2B%201)^(1/2)%20%3D%3D%2020)%3B%0A%0A%2F%2F代码中的%20dsolve%20函数用于求解微分方程,其中的微分方程应该是正确的。如果仍然存在错误,请检查输入的微分方程是否正确。%0A


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