Controlled Change in the Dimensions of an Axisymmetric Spacecraft Descending in the Atmosphere of Mars

In the presented work, a controlled change by dimensions of a spacecraft descending in the atmosphere of Mars is considered. The aim of the work is to obtain a method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions, which provides angular velocity passive control during the descent of this spacecraft in a low-density atmosphere. In the process of solving this problem, the geometric and mass-geometric characteristics of the descent spacecraft (volume, cross-sectional area, moments of inertia) were calculated. It is assumed that the outer shape of the spacecraft posterior to the incoming flow is a one-sheet rotational hyperboloid, which changes its dimensions during the spacecraft descent in the low-density atmosphere of Mars. As a result of solving the nonlinear programming problem, the minimum and maximum values of the main axial moments of inertia are obtained, which able to spin the spacecraft relative to the longitudinal axis of symmetry. The initial data for solving the nonlinear programming problem are the minimum volume and the maximum cross-sectional area of the hyperboloid, calculated according to the specified intervals of the variable controlling the dimensions of this surface. The method for calculating the mass and mass-geometric characteristics of a spacecraft when changing its dimensions ispresented, which makes it possible to control the magnitude of the angular velocity of a symmetric spacecraft in the low-density atmosphere of Mars without the use of onboard jet engines. In particular, it is shown in the work that as the height of the hyperboloid increases, the moment of inertia about the spacecraft longitudinal axis of symmetry decreases, accompanied by an increase in the moments of inertia about the transverse axes of symmetry. It can be shown that in this case there is an increase in the angular velocity of the spacecraft about the longitudinal axis, which makes it possible to achieve a stable orientation of the spacecraft upon entering the atmosphere. However, a more detailed study of the dynamics ofthe spacecraft relative motionwith a changeable shape in the atmosphere is beyond the scope of this work, but it can be presented in further publications.

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