Decomposition of a System of Equations of Motion of a Spacecraft with a Considerable Asymmetry in a Rarefied Atmosphere

Abstract

Abstract We consider a system of equations simulating an uncontrolled descent of a spacecraft in a low-density atmosphere. The spacecraft is a solid body with a shape close to a solid of revolution. An important structural feature of the spacecraft is the presence of considerable geometric and aerodynamic asymmetry in its design. It should be noted that the initial system of equations of motion for the spacecraft is essentially nonlinear. In order to enable an effective asymptotic analysis of the evolution of motion of the spacecraft, it is necessary to decompose the initial system of equations of motion of the spacecraft. The aim of this study is to decompose the system of equations of motion of the spacecraft into two subsystems: slow-motion subsystem and fast-motion subsystem. The method of integral manifolds makes it possible to lower the order of the initial system of equations. The resulting slow subsystem can be represented in the form of a single-frequency system of equations with several slow variables. An important applied result of the study is the fact that the subsequent analysis of the evolution of slow variables in a slow subsystem can be performed using known asymptotic methods.