Analysis of plane motion relative to the centre of mass of a descent capsule with the three-harmonic moment characteristics during its reentry

The paper analyses plane motion of an uncontrolled descent capsule about its centre ofmass. The aerodynamic stabilizing moment of the spacecraft by an odd Fourier series by the angle of attack with the first three harmonics. A nomogram for determining the type and number of singular points of the system phase portrait has been constructed depending on the relation of coefficients at decomposition harmonics. Analytical formulae for the action integral taken along the separatrix, expressed through elementary functions and elliptical integrals of the first and second kind have been established. Themoments of transition between various areas of the phase plane have been determined. Formulae for assessing the possibility of capture into one region or another have been established for the cases of motion when the phase point may fall into various oscillation regions when crossing the separatrix.