Vladimir S. Syromiatnikov Spacecraft Docing Devices deom SSI

The constraint equation at the point of interaction (the sum of velocities of displacements of the points of interaction of both bodies and deformations of the shock absorbers in the common normal is equal to zero): Accelerations on impact are assumed to be so large that they satisfy the expression etc. Then one can differentiate equation (5.3) ignoring the derivatives of the direction cosines, and obtain a system of three differential equations of the deformation of the shock absorbers, which have the form where is the equivalent mass defined by the expression The equivalent physical model (Figure 5.2), in which the deformation of the shock absorbers is described by the same system of equations, may be represented as the central impact of mass through three sequential shock absorbers with deformations the forces of these shock absorbers are respectively equal to

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