complex that great time and energy is required to compile and debug the computer programs and to mode! and analyze the results; moreover, when there are a large number of parameters in the model it is difficult to track the effect of individual parameters in the process as a whole. Thus, these models are needed to analyze designed docking devices, but are insufficiently efficient to synthesize them. Tn the design stage, simpler and clearer methods are needed (27, 28] which permit at least an approximate calculation of characteristics of the shock absorption system, such as forces, velocities of deformation, and the course of the shock absorbers, their energy capacity, the recovery coefficient on impact. For both main stages of shock absorption (before and after linkage) the problem of the motion and interaction of two solid bodies, which is how the spacecraft are represented (in the general case by 12 equations of motion, 6 equations of deformation and 6 constraint equations) is reduced to a study of only the deformation equations of the shock absorbers. It is further assumed that the longitudinal axis of the docking assembly coincides with one of the main axes of inertia of the bodies. The displacement of the bodies during the collision are considered small in comparison to their sizes. 5.2. Equivalent Mathematical Models of Shock Absorption Before Linkage 5.2.1. Three-Dimensional Model Let us examine the impact of two bodies with masses ; and which are absolutely solid with the exception of the vicinity of the points of interaction (T.B. in figure) (Figure 5.1). is the inertial system of coordinates, . and the systems of coordinates associated with the bodies. The axes are the main central axes of inertia. The equations of motion of the centers of mass where is the force of impact ( are projections on axes x, y, and z), directed along the normal to the surfaces of the bodies at the point of
RkJQdWJsaXNoZXIy MTU5NjU0Mg==