relative to the centers of mass are found from formulas The constraint equation unambiguously defines the displacement of the ring, that is, the vector After linkage the deformations of the longitudinal shock absorber end in several tenths of a second, and then in several seconds the deformations of the transverse shock absorbers end; at the same time the angular rotations continue for several dozen seconds. Thus, modeling of the process after linkage is expediently divided into three stages: 1} displacement of the ring in six coordinates; 2) after cessation of longitudinal displacements; 3) after cessation of transverse displacements. To model the second stage one can use the equations given above, and the component of the force of interaction is defined by some elastic deformation and rigidity , that is, — where is the residual deformation due to slippage of the friction brake. One can use another method if one assumes that there are no longitudinal deformations , and if one defines by the angular velocities of the bodies, and the component of the force by the angular velocities and accelerations. When deformations of the transverse shock absorbers cease the third section begins; here two approaches are also possible: the introduction of elastic deformations, , and with rigidities and or reduction of the number of degrees of freedom. In the second approach the constraint equation is substantially simplified and has the following form: 4.4.6. Examples of Modeling The mathematical model described above was used for work on the APDA. Tn this model a calculation was made of the parameters of the docking process with
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