The starfish experiment: a Lagrangian approach

Abstract

The present paper analyses the free surface deformation of a liquid metal drop under the influence of an alternating magnetic field. The analysis is restricted to the first axi- symmetric mode oscillation. In the low frequency case, the electromagnetic forces are of gradient type and purely oscillatory. Without any viscous damping, it is then possible to build a Lagrangian function, which involves the kinetic energy, the gravitational energy, the surface energy and the electromagnetic energy. The time evolution of the pool height is easily obtained from the Lagrange equation. It is shown that the pool height behaves like a non-linear forced oscillator.