Corresponding author: Lyubimov Vladislav V., D. Sc., Head of Higher Mathematics Department, Samara University, Samara, 443086, Russian Federation, e-mail: mail@samspace.ru

Received on January 31, 2017
Accepted on February 18, 2017

The authors consider a descent of a spacecraft capsule with small controlled aerodynamic and constant mass asymmetries in the Martian atmosphere. The aerodynamic asymmetries of the capsule are due to two controlled surfaces, which have two positions: closed and open ones. As is known, small mass and aerodynamic asymmetries of the capsule can lead to various types of resonance phenomena and effects. It should be noted that the cause of the accidents during an atmospheric descent of a spacecraft may be a resonance capture, which leads to a significant increase of the angle of attack. The purpose of this work is to provide analysis and estimation of the probability of a principal resonance capture of a capsule with small variable mass and aerodynamic asymmetries resulting in arbitrary angles of attack. The theoretical significance of this work is an approximate analytical estimation of the probability of a principal resonance capture. This estimation of the probability of a resonance capture is expressed in the terms of the elementary functions. Of practical interest is implementation of a controllable transition to the coplanar combination of the asymmetries for the capsules having an orthogonal combination of the asymmetries during a reentry. This transition may be implemented according to the introduced control law. Calculation of the probability of a resonance capture is considered on the example of the problem of the atmospheric descent of a capsule with the mass-inertial characteristics similar to the Mars Polar Lander spacecraft. The authors demonstrate that a transition from the orthogonal to the coplanar combination of the asymmetries contributes to a significant reduction of the probability of a resonance capture. The presented estimates can be used for calculation of the probability of capture or passage through a principal resonance during a descent of a spacecraft in the atmosphere of any planet.
Keywords: capsule, atmosphere, asymmetry, control, resonance, estimation, probability, Mars