— Flux -pinned interfaces maintain a passively stable equilibrium between two spacecraft in close -proximity. Although flux-pinning physics has been studied from a material s-science perspe ctive and at the systems level, the sensitivities and implications of sy stem -level designs on the dynamics need to be better understood , especially in interfa ces with multiple magnets and superconductors. These interfaces have highly nonlinear, coupled dyn amics that are influenced by physical parameters including strength of m agnetic field sources, field -cooled position, and superconductor geometry. Kordyuk’s frozen image model successfully approximates the characteristics of flux pinning dynamics but could provide more precise state prediction with the addition of these physic al parameter refinements. This paper addresses that gap by offering parametric terms to improve the dynamics model, which may better simulate the behavior of a multiple -magnet - multiple -superconductor interface. The sensitivity of the general flux -pinned dy namics model is studied by varying the physical parameters and simulating the systems level dynamics. This work represents a critical step in the development of a model suited to space craft performance verification . Index Terms —Dynamics, electromagnetic effects, superconducting magnets , close -proximity spacecraft NOMENCLATURE 𝑎#,𝑏#,𝑐#,𝑑# coefficients dictating vertical and horizontal image strength due to hysteresis 𝐵𝑎 magnetic field penetrating the superconductor at its boundary † AIAA Student M ember, Graduate Student, fz55@cornell.edu ‡ AIAA Member, Associate Professor, mp336@cornell.edu ⁎ Guidance and Control Systems Engineer, Laura.L.Jones@jp l.nasa.gov 𝐵𝑐 minimum critical threshold magnetic field 𝐵0 magnetic field surface strength of the source magnet 𝑐𝑑 rate of reduction from spatial relationship between magnet and superconductor 𝑐𝐷 coefficient of reduction from spatial relationship between magnet and superconductor 𝑐𝑔 coefficient of grain alignment, capturing the percentage of image strength at alignment 𝜃 𝑐𝑚𝑎𝑥 coefficient of reduction in which the magnet is directly centered and normal to the superconductor’s surface 𝑐𝑡 coefficient of temperature, capturing th e percentage of image stre ngth at temperature 𝑇 with respect to 𝑇𝑟𝑒𝑓 𝐹 attractive force from flux -pinned interaction ℎ vertical position of physical magnet from the surface of the superconductor 𝑘𝑙 𝑘ℎ 𝑘𝜃 stiffness in lateral, normal, and rotational degrees of freedom 𝑙 horizontal displacement of physical magnet from the center of the superconductor 𝒎𝒇 magnetic moment dipole of magnet’s frozen image 𝒎𝑭𝑪 magnetic moment dipole of physical magnet during field -cooling process 𝒎𝒉 magnetic moment dipole of magnet’s horizontal image 𝒎𝒎 magnetic moment dipole of magnet’s mobile image 𝒎𝒎𝒂𝒈 magnetic moment dipole of physical magnet 𝒎𝒗 magnetic moment dipole of magnet’s vertical image 𝑚0 maximum magnitude of magnetic moment dipole measured at 𝜃=0° 𝑚90 minimum magnitude of magnetic moment dipole measured at 𝜃=90° 𝑶𝒔 specified origin 𝝆𝒇 displacement vector from magnet’s frozen image to physical magnet 𝝆𝒎 displacement vector from magnet’s mobile image to physical m agnet 𝑞𝑥 𝑞𝑦 𝑞𝑧 𝑞𝑠 spacecraft attitude 𝒓𝒇 position vector of magnet’s frozen image from specified origin 𝒓𝑭𝑪 position vector of physical magnet during field -cooling process from specified origin 𝒓𝒎 position vector of magn et’s mobile image from specified origin 𝒓𝒎𝒂𝒈 position vector of physical magnet from specified origin 𝑇 operational temperature of the superconductor 𝑇𝑟𝑒𝑓 reference temperature of the superconductor 𝜃 relative alignment between the supercon ductor surface and magnetic moment dipole pole axis 𝜃𝐹𝐶 angular displacement from the ideal field -cooled attitude 𝑈 magnetic potential energy 𝑣𝑥 𝑣𝑦 𝑣𝑧 spacecraft velocity 𝜔𝑥 𝜔𝑦 𝜔𝑧 spacecraft angular velocity 𝜔𝑙 𝜔ℎ 𝜔𝜃 natural angular velocity in lateral, normal, and rotational degrees of freedom 𝑥 𝑦 𝑧 spacecraft position 𝑥𝐹𝐶 𝑧𝐹𝐶 spacecraft position displacement from the ideal field -cooled position TABLE OF CONTENTS 1. INTRODUCTION ................................ ................................ ................................ ................................ ........ 3 2. BACKGROUND ................................ ................................ ................................ ................................ .......... 4 3. PARAMETER IDENTIFICATION IN APPLICATION ................................ ................................ .................... 8 4. PARAMETERIZATION IN DYNAMICS ................................ ................................ ................................ ..... 14 5. SENSITIVITY STUDY OF DYNAMICS ................................ ................................ ................................ ...... 17 ACKNOWLEDGEMENTS ................................ ................................ ................................ ............................. 30