Abstract
Systems of differential motion equations perturbed by moment of external forces for spacecrafts with elastic rods and perfectly rigid bodies at their ends are constructed. Limit cycles and transition processes in the nonlinear control system with account of delay time in gas jet engines are simulated. A method of rigorous investigation of stability of limit cycles based on previously proved theorem on stable quasi-polynomial is proposed.
Similar content being viewed by others
References
S. I. Zlochevskii and E. P. Kubyshkin, “On Stabilization of a Spacecraft with Flexible Rods. II”, Kosm. Issled., 29(6), 828–839 (1991).
S. I. Zlochevskii and E. P. Kubyshkin, “On Stabilization of a Spacecraft with Flexible Rods. I”, Kosm. Issled., 27(5), 643–651 (1989).
V. I. Gulyaev, I. S. Efremov, A. G. Chernyavskii, et al., “Dynamics of a Space Station with a Long Farm”, Kosm. Issled., 32(2), 61–70 (1994).
D. K. Andreichenko and K. P. Andreichenko, “On the Theory of Stabilization of Satellites Having Elastic Rods”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., 6, 150–163 (2004) [Comp. Syst. Sci. 43 (6), 973–986 (2004)].
D. K. Andreichenko and K. P. Andreichenko, “On the Theory of Hybrid Dynamical Systems”, Izv. Ross. Akad. Nauk, Teor. Sist. Upr., 3, 54–69 (2000) [Comp. Syst. Sci. 39 (3), 383–398 (2000)].
L. A. Lusternik and V. I. Sobolev, A Brief Course of Functional Analysis (Moscow: Vysch. Shkola, 1982).
B. P. Demidovich, Lections on Mathematical Stability Theory (Moscow, Izd. MGU, 1998) [in Russian].
G. A. Korn and T. A. Korn, Mathematical Handbook for Scientists and Engineers, (McGraw-Hill, New York, 1961; Nauka, Moscow, 1973).
D. K. Andreichenko, “An Efficient Algorithm of Numerical Inversion of Integral Laplace Transform”, Comput. Math. Math. Phys., 40(7), 1030–1044 (2000).
Author information
Authors and Affiliations
Additional information
Original Russian Text © D.K. Andreichenko, K.P. Andreichenko, 2007, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2007, No. 5, pp. 137–149.
Rights and permissions
About this article
Cite this article
Andreichenko, D.K., Andreichenko, K.P. On stability of limit cycles in stabilization systems of spacecrafts with elastic rods. J. Comput. Syst. Sci. Int. 46, 802–814 (2007). https://doi.org/10.1134/S1064230707050127
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/S1064230707050127