This paper develops a new implicit solution procedure for multibody systems based on a three-sub-step composite method, named TTBIF (trapezoidal–trapezoidal backward interpolation formula). The TTBIF is second-order accurate, and the effective stiffness matrices of the first two sub-steps are the same. In this work, the algorithmic parameters of the TTBIF are further optimized to minimize its local truncation error. Theoretical analysis shows that for both undamped and damped systems, this optimized TTBIF is unconditionally stable, controllably dissipative, third-order accurate, and has no overshoots. Additionally, the effective stiffness matrices of all three sub-steps are the same, leading to the effective stiffness matrix being factorized only once in a step for linear systems. Then, the implementation procedure of the present optimized TTBIF for multibody systems is presented, in which the position constraint equation is strictly satisfied. The advantages in accuracy, stability, and energy conservation of the optimized TTBIF are validated by some benchmark multibody dynamic problems.

The docking mechanism is a key component for on-orbit refueling technology. In this paper, the design and analysis of a novel floating docking mechanism for on-orbit berthing-based refueling is presented. Compared with traditional berthing and docking, the berthing here is high in success rate and low in impact, which is accomplished by stretching out a docking subassembly instead of pulling back the client spacecraft. However, the berthing also has two problems: initial deviations between two spacecraft and an additional force generated by a hard alloy refueling pipe, which both seriously affect the docking operation. Thus, the docking mechanism is designed to have alignment abilities and decrease the additional force as much as possible. Based on the principles above, we introduced spring pins and a helical refueling pipe to design a light, compact, and simple docking mechanism. To further reduce the additional force, we proposed an elliptical-helical pipe and analyzed its mechanical properties. Finally, simulations and experiments were conducted to validate the proposed mechanism. The results show that the proposed mechanism with an elliptical-helical pipe has a high tolerance for linear and angular misalignment and superior dynamic performance during docking.

With the development of aerospace technology, rigid-flexible coupling spacecraft with strong nonlinearity dominates, bringing huge challenges for numerical tools. This paper aims to accurately and quickly analyze the dynamic behavior of rigid-flexible coupling spacecraft. In our work, rigid body and flexible body are both described by Euler parameters for avoiding singular angles. Then, for this type of strong nonlinear dynamic system, the BN-stable method that is unconditionally stable for nonlinear initial value problems proposed by the first author is introduced to solve the transient responses. To keep the accuracy of the numerical rotation matrix, the relation between the angular velocity and Euler parameters, and the constraint in the level of velocity, are introduced to reformulate the original BN-stable method. Through the dynamic analysis for rigid satellite bodies and flexible solar wings, we find that the proposed strategy can effectively simulate the dynamic responses of spacecraft, and compared to the currently popular strategy, our strategy enjoys considerable advantages in accuracy, stability, and dissipation.