4.3.3. Choice of Initial Conditions for Modeling The parameters of initial conditions are usually random values; thus, to analyze the docking process it is expedient to use statistical methods. Tn practice the task is complicated by the fact that the number of random parameters is relatively large, and in spatial models the relative position and velocity are given by 11 and frequently 14 parameters. Due to the complexity of the mathematical models solution on a computer requires a significant amount of machine time. To reduce machine time use, very simple models are used which describe the motion of the bodies with impact interaction. For further simplification, two-dimensional flat bodies are examined. This makes it possible to significantly reduce the number of equations of motion and the number of varied parameters of initial conditions. In planning, one may also vary inertial and geometric characteristics of the spacecraft and docking device, for example, the angle of conicity and the coefficient of recovery during impact. Another important task of statistical analysis is the determination of critical (worst) combinations of initial conditions in which maximum momenta arise or during which docking will not occur. These combinations are usually realized at maximum initial displacements in different coordinates and at extreme velocities (maximum and minimum). Thus, to reduce the number of combinations in the selection of initial parameters it is expedient to use laws for their random distribution, which insures the manifestation of these parameters at the “edges” of the range with highest probability, and those close to the mathematical expectation at the “edges” of the range with the lowest probability. The determined critical combinations of initial conditions are used for analysis with more complete mathematical models and in comprehensive dynamic testing. This approach makes it possible to reduce the number of calculated cases and reduce the risk of missing important combinations.
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