VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University93810.18287/2541-7533-2010-0-4(24)-11-19UnknownResearch of spatial motion of an uncontrolled spacecraft with the triharmonic moment characteristics around its center of mass during its reentry into atmosphereBarinovaYe. V.<p>Post-graduate Student</p>15545@yandex.ruTimbayI. A.<p>Doctor of Technical Science, Professor</p>
<p>Head of the Department of Higher Mathematics</p>timbai@ssau.ruSamara State Aerospace University1812201094111920062014Copyright © 2015, VESTNIK of the Samara State Aerospace University2015<p>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.</p>Spacecraftrestoring aerodynamic momentphase portraitseparatrixaction integralprobabilityСпускаемый аппаратаэродинамический восстанавливающий моментфазовый портретсепаратрисаинтеграл действиявероятность[1. Kuzmak, G. E. Dynamics of Uncontrolled Motion of Spacecraft at Their Reentry into the Atmosphere [Text] / G. E. Kuzmak. – Moscow: Nauka, 1970.][2. Yaroshevskii, V. A. Motion of an Uncontrolled Body in the Atmosphere [Text] / V. A. Yaroshevskii. – Moscow: Mashinostroenie, 1978.][3. Aslanov, V. S. Transient Modes of Spacecraft Angular Motion on the Upper Section of the Reentry Trajectory [Text] / V. S. Aslanov, I. A. Timbai // Kosm. Issled., 1997, vol. 35, no. 3, p. 279 – 286.][4. Barinova, E. V. Research of Planar Motion of an Uncontrolled Spacecraft with the Treegarmonic Moment Characteristics around its Center of Mass at its Reentry into Atmosphere, [Text] / E. V. Barinova, I. A. Timbai // Vestnik SSAU, 2010, no. 1 (21), p. 9 – 19.][5. Aslanov, V. S. Space Motions of a Reentry Spacecraft in the Atmosphere [Text] / V. S. Aslanov. – Moscow: FIZMATHLIT, 2004.][6. Neishtadt, A. I., Variation of Adiabatic Invariant Crossing the Separatrix [Text] / A. I. Neishtadt // Fiz. Plazmy, 1986. vol.12. no. 8. p. 992 – 1001.][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.]