vectors from the second and third systems of coordinates into the first. The condition of equilibrium of the rod gives the system of equations where sin the unit vectors and are defined by the columns of the appropriate matrices and Equations (4.13) and (4.14) along with equation and equations of motion (4.11) and (4.12) form a system to find all unknown parameters of the process. After displacement of the longitudinal shock absorber ceases, the problem may be solved in two ways. One can, as before, use the described system of equations, defining force by some elastic deformation , that is, where is the rigidity of the structure in the longitudinal direction. In the second method it is assumed that and the relative position of the center of mass of body 2 in system of coordinates 1 is defined by five independent coordinates , and the force of interaction is calculated using angular accelerations. 4.4. Mathematical Models Tor Peripheral Devices Mathematical models of docking dynamics for peripheral docking devices, the same as for “rod and cone” devices, consist of two parts, due to the significant properties of constraints before and after linkage. The most complex for these docking devices is the task of finding the points of interaction for a large number of possible combinations of elements of the rings with guide protrusions. Below we present the principle for constructing a mathematical model based on the example of a model developed to analyze the docking process using the Soyuz APDA (16]. The model is given in a form which is convenient for subsequent transformation to consider the inertia of the shock absorbers.
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