Research On Dynamic Modeling And Simulation Of Variable Constraint Docking

Docking process of the space vehicles is the typical problem of dynamics of multi-body systems, which can be modeled by Newton-Euler method or Lagrange multiplier method. But In the process of the docking collision, there are many multi-point contact, so system degrees of freedom is time varying, which leads to system constraint equations is time varying. That's why the kinetic equations are time varying and differential-algebraic which is built by Newton-Euler method or Lagrange multiplier method. At present, what is for the treatment of this question is eliminating binding and reducing dimension of system. But in the process of space docking, it's too hard to find a set of generalized coordinates to reduce the dimension of original system because of the complexity of the space vehicles and the uncertainty of the docking collision, so many methods in the solution of Euler-Lagrange equations become useless.Address these issues, this article proposed the general process and principle for solving differential-algebraic questions, then used null space principle to solve docking dynamic equation. In the null space principle, by means of Gram-Schmidt we can get a group of space-based vectors and bull space of Jacobi matrix. Then through a series of mathematical methods, we can get a group of system generalized coordinates to reduce the dimension of original system to solve system kinetic equations. Finally, using Matlab simulation software verificated the docking dynamics model and null space principle and the result of four sets of initial conditions demonstrate the correctness of the docking dynamics model and null space principle.