Prove that Stodola's criterion is necessary but not sufficient. That is, 1. If all roots of a cubic polynomial belong to the left half-plane, then all coefficients have the same sign, but 2. There are polynomials of degree 3 whose all coefficients are positive, but some roots belong to the right half-plane.
Hurwitz criterion belongs now to the standard engineering curriculum.
Earlier, in 1868, the question was investigated by the famous physicist J.C. Maxwell, who found a correct solution for polynomials of 3-d degree. Hurwitz's criterion is considered more convenient by the engineers. Turbines are the most efficient way of converting heat into mechanical work. Most electric power stations and large ships use steam turbines. Most airplanes use gas turbines.