Data-Fitted Approximate Analytical Torque Model for Electromagnetic De-Tumbling of a Nutating Conducting Spherical Shell under Bounded Positional Offsets

Electromagnetic de-tumbling has emerged as a promising non-contact approach for mitigating the rotational motion of space debris and defunct satellites because of its inherent safety and controllability. In practical missions, however, the target often undergoes nutational motion and bounded positional offsets relative to the service spacecraft, which makes rapid and accurate prediction of electromagnetic torque more difficult. This paper presents a corrected approximate analytical model for calculating the electromagnetic torque acting on a nutating conducting spherical shell in a magnetic dipole field within a bounded offset domain. A mathematical model describing the relative position and electromagnetic interaction between the spherical shell and the magnetic dipole is first established. Finite-element simulations are then conducted to obtain the spatial distributions of the three torque components and to provide numerical benchmarks. Based on these results, approximate analytical expressions and polynomial correction terms are derived for torque prediction. The corrected analytical solutions show high accuracy and good consistency with the numerical results, providing an effective theoretical basis for subsequent dynamic analysis, real-time control, and rapid torque prediction.