01
Solve the ODE
Solve (algebraically) the ODE used to define the catenary curve.
(Hint: differentiate the function , substitute in, then use a reduction of order.)
02
Arch vs. chain
Why does the St. Louis arch (or any other self-supporting arch) also have a catenary shape?
03
Pushing a pole
Suppose a pole is pushed from one end, with a free pivot on the end from which it is pushed. The shape of the path taken by the opposite end is also a tractrix. Why?
(Describe the concept of tractrix in such a way that it applies equally to dragging strings and pushing poles.)
04
Checking algebra
Check the algebra for the solution of and then the integration for . (Write out all intermediate steps.)