Question

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

Answer 1

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]