# Multi-Body Dynamics Modeling and Simulation of Maglev Satellites
## 1 Introduction  
In order to improve the ground imaging capability of spaceborne payloads, current space missions have proposed the ability requirements for ultra-precision pointing and ultra-stable control of spaceborne imaging payloads [1]. The traditional connection method between the satellite body and the imaging payload is through mechanical bearings. Compared with mechanical bearings, magnetic levitation bearings have a longer service life, do not wear, do not require lubrication, and possess controllable dynamic characteristics. They can reduce the influence of high-frequency vibration in the satellite body on the pointing control of the imaging payload and improve the pointing control accuracy of the imaging payload [2, 3].  
Compared with magnetic resistance magnetic bearings, Lorentz force magnetic bearings have no iron loss, good linearity, larger control bandwidth, and higher control accuracy, and are an ideal suspension method in microgravity environments [4]. The Canadian Space Agency has developed a series of MIM systems that utilize Lorentz force actuators to achieve activation control, which can isolate small vibrations in the range of 0.01 Hz to 100 Hz and have been successfully applied to the MIM Space Station [5]. In 2016, [PERSON] et al. from Israel designed a high-precision positioning table iterative learning output controller with travel range limitations for a 6-DOF maglev platform with uncertain loads, ensuring that all balance points are within the system's motion range [6].  
In 2017, [PERSON] et al. from Columbia University proposed a 6-DOF (Degrees of Freedom) magnetic levitation turntable for precision positioning. The turntable uses Lorentz force to provide driving force, which can provide sub-micron accuracy in precision micro-machining applications [7]. The precise vacuum-compatible dual servo maglev platform developed by the Seoul team in South Korea in 2022 can achieve an accuracy of 10 nm [8].  
[PERSON] et al. have developed a set of 6-DOF vibration isolation equipment with reference to the MIM gravity vibration isolation equipment. At present, a prototype has been made, and good results have been achieved in experiments [9]. [PERSON] from the Shanghai Satellite Engineering Research Institute studied a collaborative control method for the isolation of payload modules and platform modules, using the DFP (Disturbance Free Payload) satellite platform as a reference. They achieved high pointing accuracy and stability in attitude control, and verified the performance of the platform through mathematical simulation [10]. The Beijing 3 satellite adopts a magnetic levitation precise isolation platform \(10^{\circ}/\)s to achieve three super performance, with a maximum in orbit attitude maneuver of and a stability of the entire satellite attitude angular velocity better than \(2\times 10^{-5}/\)s [11].  
For magnetic levitation systems, the performance of linear controllers can only be accepted at the equilibrium point, and selecting nonlinear controllers can provide global stability to the system [12]. Quaternions, as an effective mathematical tool for describing rotation, are widely used in attitude control of magnetic levitation systems.  
Magnetic levitation satellites have shown significant advantages in active vibration isolation. The Lorentz force maglev gimbal stable platform (LFMP), as a new generation of satellite payload platform for rapid spatial information acquisition, precise pointing and positioning, and continuous control and disturbance reduction, requires ultra-stable, ultra-static, and ultra-agile technologies as its core features.