求下列参数方程所确定函数的二阶导数:x=a(t-sint),y=a(1-cost)

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求下列参数方程所确定函数的二阶导数:x=a(t-sint),y=a(1-cost)

求下列参数方程所确定函数的二阶导数:x=a(t-sint),y=a(1-cost)
求下列参数方程所确定函数的二阶导数:x=a(t-sint),y=a(1-cost)

求下列参数方程所确定函数的二阶导数:x=a(t-sint),y=a(1-cost)
dx/dt=a(1-cost)
dy/dt=asint
y'=sint/(1-cost)
dy'/dt=[cost(1-cost)-sint*sint]/(1-cost)^2=(cost-1)/(1-cost)^2=-1/(1-cost)
y"=(dy'/dt)/(dx/dt)=-1/[a(1-cost)^2]