Beitrag zur Kenntnis der Eigenschwingung einer idealen Flüssigkeit in kommunizierenden Röhren

Summary

The oscillation of an ideal liquid in communication tubes of arbitrary shape leads to a non-linear differential equation of second order. The coefficient of the second derivative is a linear function of the displacement, and furthermore the differential equation is not linear, because a quadratic term in the first derivative appears.

The equation becomes linear if and only if the cross sections at the ends of the liquid column are constant but not equal, the periods of oscillation in the two directions are different and the difference increases monotone with increasing amplitude of the displacement.