求摆线的参数方程x=a(t-sint) 和 y=a(1-cost)所确定的函数y=y（x）的
求摆线的参数方程x=a(t-sint) 和 y=a(1-cost)所确定的函数y=y（x）的二阶导数 .答案是-1/a(1-cost)^2
简单分析一下，答案如图所示
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第1个回答 2019-02-28
dx/dt=a(1-cost)
dy/dt=asint
y'=dy/dx=(dy/dt)/(dx/dt)=sint/(1-cost)
dy'/dt=[cost(1-cost)-sint(sint)]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost)
y"=dy'/dx=(dy'/dt)/(dx/dt)=-1/(1-cost)/[a(1-cost)]=-1/[a(1-cost)^2]
dy/dt=asint
y'=dy/dx=(dy/dt)/(dx/dt)=sint/(1-cost)
dy'/dt=[cost(1-cost)-sint(sint)]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost)
y"=dy'/dx=(dy'/dt)/(dx/dt)=-1/(1-cost)/[a(1-cost)]=-1/[a(1-cost)^2]
