The dynamical behavior of a spherical pendulum in a ferrofluid volume influenced by a magnetic force

The paper deals with a spherical pendulum inside a spherical ferrofluid volume in the presence of an uniform magnetic field. The problem is motivated by biological tactile sensors of mammals. These thin long hairs, called vibrissae, grow from a special follicle incorporating a capsule of blood and are used by mammals for exploration of the surrounding area. We propose a continuum model of the viscoelastic support of a vibrissa inside the follicle as a spherical volume filled with ferrofluid. It is a stable colloidal suspension of nanoscale ferromagnetic particles in a viscous carrier liquid. The tactile hair is modeled as a rigid rod with a spherical body at the end, which is submerged inside the ferrofluid. Using analytic expressions for the magnetic force acting on a paramagnetic body in the presence of an uniform magnetic field, Euler’s equations of motion of the spherical pendulum are derived. The conditions for the maximum possible magnitude of the magnetic force acting on the body are analyzed. It is shown that the dynamical behavior of the pendulum may be controlled by means of an uniform applied magnetic field. The results are important for the development of artificial tactile sensors.