THE STARFISH EXPERIMENT: A LAGRANGIAN APPROACH

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. Introduction. When a liquid metal drop is submitted to a vertical alter-nating magnetic field, it tends to oscillate in a horizontal plane. This phenomenon has been put forth in the so-called “Starfish experiment ” (Daugan et al. [1], In-gwiller et al. [2]). According to the magnetic field strength and its frequency f, various types of motions have been observed. For weak magnetic field intensities