## 1 Introduction  
The development of the human spaceflight industry is threatened by a huge amount of space debris, such as residual rocket stages, uncooperative satellites, disintegrated spacecraft, and collision derivatives [1]. As of 2017, the total number of space debris pieces in the Earth's orbit is in the tens of billions [2]. Large space debris, such as rocket final stages and failed satellites, weigh more than 1000 kg and rotate at speeds of more than 25\({}^{\circ}\)/s. Super-high-speed collisions could occur between them, which would lead to the formation of large-area high-speed debris clouds [3]. The damage caused by large space debris is huge, and they are difficult to remove. The National Aeronautics and Space Administration's statistics show that if two debris were removed each year starting from 2020, the growth trend of the number of debris would significantly reduce. If five debris were removed each year starting from 2020, the growth trend would stabilize [4]. The active removal of space debris is the only effective way to completely curb the increase in the number of debris. Therefore, the active removal of space debris is currently one of the hot topics in the field of space research. Capturing debris in orbit is the key to active removal, however, this is quite difficult to achieve, because the motions of space debris are very complicated. Space debris are affected by such factors as space perturbation force or torque and residual angular momentum before failure, and are often in a state of high speed and complex tumbling motion [5]. If the angular momentum of the target is reduced before the target is captured, it is relatively easy to directly capture the target. Detumbling of space debris actually refers to the process of using external control torque to attenuate the target angular velocity, thereby stabilizing the target attitude. Detumbling of space debris can be divided into contact and noncontact depending on whether the force is in contact with the target. Contact detumbling mainly includes the use of a deceleration brush, mechanical impact, a tether robot, and so on. Noncontact detumbling includes the use of gas, electrostatic force, electromagnetic force, an ion beam, a laser, and other methods, and has the advantages of long operating distance, high safety, and strong attitude tolerance. It is also able to provide multi-degree-of-freedom acting torque, but its impact force is generally in the order of mN [5]. For large space debris with large mass and high speed, noncontact detumbling requires dozens or even hundreds of hours at low efficiency, which causes the energy loss of the device to increase and the number of reuses to be reduced. Contact detumbling provides greater control force, usually reaching the order of N [5]. Among the different methods, mechanical impact provides the largest braking force, which is a very efficient method of active detumbling. JAXA's [PERSON] and [PERSON] proposed to eliminate rotation before capture using the elastic contact force between a deceleration brush and the target [6]. [PERSON], of the national aeronautics and space laboratory of Japan, used alternating attenuation of the target nutation angle and self-rotation velocity by multiple contact pulse forces [7]. [PERSON] used a viscoelastic rope system attached to the rotating space debris surface and controlled the target speed until its attitude was stable through rope tension and damping force during deformation [8]. [PERSON], of the Tokyo institute of technology, took the elastic ball as the end-effector of a mechanical arm and used the normal impact force and friction force generated by the elastic impact between the mechanical arm and the target surface to attenuate rotation [9]. In the existing research on mechanical impact detumbling, a constant pressure-based impact model established by [PERSON] was adopted by many researchers.