Abstract
Returning from orbit to a surface of a planet is one of the most difficult and important problems of modern astronautics. This chapter explores uncontrolled descent of the reentry capsule into an atmosphere. We discuss the aerodynamic features of reentry capsules of various shapes. Equations of motion in the atmosphere for the axisymmetric and asymmetrical capsule are given in this chapter. Analytic solution for the unperturbed motion of the capsule under the influence of sinusoidal aerodynamic moment is obtained. For the case of biharmonic aerodynamic moment, the qualitative analysis of the phase portrait and analytic solutions for the unperturbed motion is given. Quasistatic solutions for the disturbed motion are obtained. Adiabatic invariants and the approximate solutions for the disturbed motion of the reentry capsule under influence of the sinusoidal and biharmonic restoring moments are found. The perturbed motion of the capsule is studied by the averaging method. It is shown that numerical integration of equations of perturbed motion does not allow to receive authentic results because of stochastic character of motion. Calculation procedure, which allows to obtain all possible variants of motion, is given there. Chaotic motions of the reentry vehicle with an internal moving mass, bodies in a resistant medium, and asymmetrical reentry capsule in the atmosphere are studied by the Melnikov function and Poincaré sections. Analytic solutions for homoclinic orbits of biharmonic system are obtained. The algorithm for the selection of the damping coefficient, in order to eliminate the chaotic motion during the reentry capsule descent, is given in this chapter.
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