Vibrations of a frameless film membrane stabilized by the Ampère force in zero gravity

The dynamics of a circular film membrane with attached current-carrying conductors in zero gravity is studied. Equations are derived which describe the vibrations of the membrane stabilized by the Ampère force. The spectrum of natural vibrations and their corresponding strains are calculated. Constrained vibrations of the membrane are studied. The effect of the geomagnetic field on the stability of the membrane and the damping of its vibration is investigated for unsteady modes of application of mechanical forces in zero gravity.