Research of spatial motion of an uncontrolled spacecraft with the triharmonic moment characteristics around its center of mass during its reentry into atmosphere

Abstract

Spatial motion of an uncontrolled spacecraft around its center of mass is considered, the restoring aerodynamic moment of the spacecraft being described by an odd Fourier series in the angle of attack with the three first harmonics. Analytical formulas are deduced for the action integral along seperatrix, expressed, in terms of elliptic integrals of the first, second and third kind and of elementary functions. The moments of transition between various phase planes are determined. Formulas for determining the probability of capture into any region are deduced. The moments of additional equilibrium state appearing on the phase plane are determined. The analytical condition that determines the initial angular velocity ensuring the absence of additional equilibrium states ou the angle of attack in the given time interval is specified.

About the authors

Ye. V. Barinova

Samara State Aerospace University

Author for correspondence.
Email: 15545@yandex.ru

Post-graduate Student

Russian Federation

I. A. Timbay

Samara State Aerospace University

Email: timbai@ssau.ru

Doctor of Technical Science, Professor

Head of the Department of Higher Mathematics

Russian Federation

References

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  7. Lifshits, I. M. Features of Charged Particle Motion in Changing and Inhomogeneous Electromagnetic Fields [Text] / I. M. Lifshits, A. A. Slutskin, V. M. Nabutovskii // Zh. Eksp. Teor. Fiz., 1961, vol. 41, no. 3, p. 939 – 948.

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