设参数方程x=t(1-sint);y=tcost , a为常数, 求二阶导数 d^2y/(dx^2)
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设参数方程x=t(1-sint);y=tcost , a为常数, 求二阶导数 d^2y/(dx^2)
![设参数方程x=t(1-sint);y=tcost , a为常数, 求二阶导数 d^2y/(dx^2)](/uploads/image/z/16117040-56-0.jpg?t=%E8%AE%BE%E5%8F%82%E6%95%B0%E6%96%B9%E7%A8%8Bx%3Dt%281-sint%29%3By%3Dtcost+%2C+a%E4%B8%BA%E5%B8%B8%E6%95%B0%2C+%E6%B1%82%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0+d%5E2y%2F%28dx%5E2%29)
dy/dx=(dy/dt)/(dx/dt)=(cost-tsint)/(1-sint-tcost)
d^2y/dx^2=(dy/dx)/(dx/dt)
=[(-sint-sint-tcost)(1-sint-tcost)-(cost-tsint)(-cost-cost+tsint)/(1-sint-tcost)^3
=[(2sint+tcost)(sint+tcost-1)+(cost-tsint)(2cost-tsint)]/(1-sint-tcost)^3
后面的展开计算化简了.
d^2y/dx^2=(dy/dx)/(dx/dt)
=[(-sint-sint-tcost)(1-sint-tcost)-(cost-tsint)(-cost-cost+tsint)/(1-sint-tcost)^3
=[(2sint+tcost)(sint+tcost-1)+(cost-tsint)(2cost-tsint)]/(1-sint-tcost)^3
后面的展开计算化简了.
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