where are the initial values of these angles. Transformation of the components of vectors from the third to the first system of coordinates is done using a matrix which is obtained from matrix by replacing and 9 with , and (respectively the angles of roll, yaw, and pitch of the rotation of system of coordinates 3 relative to system of coordinates 1). To reduce the presentation the majority of the equations are written below in vector form. In real models for calculations on computers, equations of the projections are used; thus, indicating the required transformation of vectors with the appropriate matrices. Indications of the number of unknowns and their equations also infer the number of projections of unknown vectors. 4.3. Models for the “Rod and Cone” Docking Device 4.3.1. Modeling with Impact Interaction In these simplified models it is also assumed that the speed of the spacecraft during interaction varies instantaneously without a change in position; thus, the effect of other forces is negligibly small. The points of interaction are defined as points of interaction of the “lengthened” rod (Figure 4.1), which is given by a radius vector lengthened by w (w is the parameter) with a conical surface also given in parametric form; the projection of vector from the vertex of the cone is at this point equal to The parameters are defined from the vector equation
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