Linearized Dynamics of General Flux-Pinned Interfaces

Abstract

A flux-pinned interface offers a passively stable equilibrium that otherwise cannot occur between magnets because electromagnetic fields are divergenceless. The contactless, compliant nature of flux pinning offers many benefits for close-proximity robotic maneuvers, such as rendezvous, docking, and actuation. This paper derives the six degree-of-freedom linear dynamics about an equilibrium for any magnet/superconductor configuration. Linearized dynamics are well suited to predicting close-proximity maneuvers, provide insights into the character of the dynamic system, and are essential for linear control synthesis. The equilibria and stability of a flux-pinned interface are found using Villani's equations for magnetic dipoles. Kordyuk's frozen-image model provides the nonlinear flux-pinning response to these magnetic forces and torques, all of which are then linearized. Comparing simulation results of the nonlinear and linear dynamics shows the extent of the linear model's applicability. Nevertheless, these simple models offer computational speed and physical intuition that a nonlinear model does not.