设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2答案是-1/a(1-cost)^2

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 00:03:12
设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2答案是-1/a(1-cost)^2

设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2答案是-1/a(1-cost)^2
设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2
答案是-1/a(1-cost)^2

设X=a(t-sint) Y=a(1-cost) ,求d^2y/dx^2答案是-1/a(1-cost)^2
不好意思,计算失误,重新计算了一遍.
dy/dt=asint
dx/dt=a(1-cost)
dy/dx=(dy/dt)/(dx/dt)=sint/(1-cost)
d(dy/dx)/dt=(cost-1)/(1-cost)^2
(d^2y)/(dx^2)=[d(dy/dx)/dt]/(dx/dt)=[(cost-1)/(1-cost)^2]/a(1-cost)=-1/a(1-cost)^2