A simplified model of tethered projectile systems wrapping around targets in space and a preliminary capture scheme based thereon

The Euler-Eytelwein equation indicates that the tension from one end of the rope to the other end decays exponentially with the wrapping angle after wrapping around a target object, and the tensions at two ends can differ by several orders of magnitude. The ability to scale the force magnitude of this wrapping structure may be exploited for space captures. This paper simplifies the modeling of the actual scene of space capture, analyzes the kinematic characteristics of the wrapping process of tethered projectile systems, and obtains the trajectory equation of the projectile. Carrying out the force analysis of the element, forces acting on the satellite and the target object under different friction coefficients are obtained. Finally, considering two constraints of rope tension and wrapping time, as well as the number of wrapping turns for safe, a design scheme of projectile velocity and initial rope length required for successful capture is proposed.