This case may be represented in the form of an impact of mass cos . cos through a spring with rigidity and a lateral shock absorber. Figure 5.12 shows the changes in rom the angle between the longitudinal axes for the docking of two Soyuz spacecraft . The initial velocities of deformation of the spring and shock absorber are defined by the formulas Analysis shows that for large values of fl., the velocity of deformation increases substantially, for example, for = . The total force for an impact , thus for large 4/ and damping proportional to velocity, force also increases to values which are times greater than for a shock absorber which is deformed along the normal to the shape of the cone (for the examined docking device, by about a factor of two). For a larger angle of the half-aperture of the cone (for the Soyuz-Salyut docking device the increases in the rate of deformation and force are significant. In damping proportional to the square of the velocity force increases even more. The increase in the rate of deformation and the force of impact when . increases is one of the main drawbacks of a system without an initial stage in the longitudinal shock absorber. Moreover, the energy capacity of the lateral shock absorbers should be increased substantially. Figure 5.13 shows the dependence of the coefficient of recovery s (for constant parameters of the Soyuz docking mechanism shock absorbers) on the angle between the longitudinal axes of the spacecraft. When damping is proportional to velocity, as decreases the coefficient of recovery increases; thus, as decreases decreases rapidly) the coefficient increases several times. Figure 5.13 shows the dependence of on the coefficient of attenuation ; it is obvious that there is an optimal value of at which s is minimal. The presence of an optimal value is characteristic for impact through sequentially arranged springs and a damped shock absorber. For each there is an optimal and a minimal attainable value of the recovery coefficient .
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