Motion of a falling drop with accretion using canonical methods

Abstract

The motion of a falling drop whose mass grows by accretion is studied with canonical methods. This approach requires the introduction of S-equivalent non natural Lagrangians. That is, we have to consider Lagrangians that give rise to equations of motion that are not exactly the same as the equations of interest, but anyway they share the same solutions. We study three examples of laws of accretion: mass growing linearly with time, mass growing linearly with the surface of the drop, and mass growing proportionally to the product of surface and velocity of the drop. In all cases we recover the results obtained by means of the Newtonian methods, which we expose in table I.