interaction is examined in the form of the exchange of impact momenta. Tn these models it is expedient to conduct statistical studies. The critical combinations determined in these models may be used for detailed calculations in more complex models. 4.2. Structures of Models, Assumptions, Systems of Coordinates The most complex mathematical model is that for the first stage of docking before linkage. The problem is divided into several parts: 1) determination of the points of interaction; 2) description of the constraints; 3) search for reactions; 4) determination of the effect of the control system; 5) solution of the equations of motion. The points of interaction are defined as points of intersection of lines or surfaces (by methods of analytical geometry). Using these methods the directions of reactions are defined, as well as the constraint equations. Deformation of the shock absorbers and their derivatives are defined by reaction values. The spacecraft in these models are usually represented by solid bodies. The elasticity of the spacecraft construction, its individual parts, and the liquid filling the tanks, as a rule, do not have a substantial effect on the dynamics of docking. If necessary their effect can be estimated. To analyze docking with a “rod and cone” type docking device two- dimensional and spatial models are used. Tn the creation of peripheral docking devices only spatial models are necessary. Shock absorbers, as a rule, are considered noninertial. However, a consideration of the inertia of the moving parts of the shock absorbers is necessary for an accurate determination of loads during docking with electromechanical docking mechanisms. Friction at the points of interaction are frequently neglected, since the equations which consider them complicate the spatial model significantly. Even a flat model which considers friction is rather complex. A model of the second stage of docking (after linkage) is usually substantially simpler.
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