Computer-Based Derivation and Transformations of Spatial Motion Equations of a Large Space Structure in the Course of Its Assembly

摘要

A mechanic system of the form of a large space structure being assembled in orbit is considered. The problem of on-line computer-based derivation of the current mathematical model of the spatial motion of a mechanic system with its structure changing when extra bodies or constraints are either added or removed is studied. The problem is solved using Lagrange equations of second kind. In the problem statement, it is required that the computing system linearize the obtained nonlinear Lagrange mathematical model, transform it by reducing it to the principal (normal) coordinates and then pass to more constructive, in terms of synthesizing control laws, modally physical representation. The mathematical technique for solving the listed problems is given. A number of necessary propositions are proved. The examples are given to illustrate that the proposed methods are constructive and can be implemented sufficiently simply in Maple.