Stability investigation of the steady motions of an isolated system, carrying out plane motion
DOI:
https://doi.org/10.15587/1729-4061.2015.49269Keywords:
lifting body, pendulums, motion stability, spacecraft, passive autobalancer, damperAbstract
The paper investigates the conditional stability of steady motions of a flat model of an isolated system consisting of a rotating LB, material point, which creates its static imbalance, and two identical mathematical pendulums, mounted on the longitudinal axis of the LB and moving in the plane of the static imbalance, the relative motion of which is prevented by the viscous resistance. It was found that in the case where there is imbalance and pendulums can eliminate it with a certain reserve, there is one basic motion; in the absence of imbalance, there is a one-parameter family of basic motions; in the case of maximum imbalance, which can be eliminated by pendulums, there is one basic motion, but it generates pseudo-family of basic motions. Also, it was found that some basic motions are conditionally asymptotically stable, if they, or family, or pseudo-family of basic motions are isolated. In the absence of imbalance, the presence of a single zero root of the characteristic equation does not affect the stability of the one-parameter family of basic motions, and is responsible for the transition from one to another steady motion of the family. In the case of maximum imbalance, the presence of a single zero root of the characteristic equation does not affect the stability of the basic motion, and is responsible for the transition from one to another steady motion of pseudo-family. Transients, depending on the system parameters can be aperiodic or oscillatory-damped. It was found that the side motions are unstable.
References
- Artjuhin, Ju. P., Kargu, L. I., Simaev, V. L. (1979). Control systems of spacecraft stabilized rotation. Moscow: Nauka, 296.
- Kargu, L. I. (1980). Systems angular stabilization of spacecraft. Moscow: Mashinostroenie, 172.
- Popov, V. I. (1986). Systems of orientation and stabilization of spacecraft. Moscow: Mashinostroenie, 184.
- Zinchenko, O. N. (2011). Small optical satellites DZZ. Available at: http://www.racurs.ru/www_download/articles/Micro_Satellites.pdf
- Ovchinnikov, M. Y. (2007). Small this world. Kompyuterra, 15, 37–43. Available at: http://old.computerra.ru/2007/683/315829/
- Blinov, V. N., Ivanov, N. N., Sechenov, Ju. N., Shalaj, V. V. (2010). Small spacecraft. The 3 books. Bk. 3: the mini-satellite. Unified space platform for small satellites: handbook. Omsk: Omsk State Technical University, 348.
- Fateev, V. F. (Ed.) (2010). Small spacecraft information provision. Moscow: Radiotehnika, 320.
- Gidlund, S. (2005). Design Study for a Formation-Flying Nanosatellite Cluster. Available at: http://epubl.ltu.se/1402-1617/2005/147/
- Small Spacecraft Technology State of the Art (2014). Available at: https://www.nasa.gov/sites/default/files/files/Small_Spacecraft_Technology_State_of_the_Art_2014.pdf
- Makridenko, L. A., Volkov, S. N., Hodnenko, V. P. et al. (2010). Conceptual questions of creation and application of small satellites. Questions of Electromechanics. Proceedings VNIIEM, 114 (1), 15–26.
- Gritsenko, A. A. (2001). Using stabilized rotation of small satellites in the satellite communication systems for GEO and HEO orbits. Available at: http://www.spacecenter.ru/Resurses/IEEE_2001_2.doc
- Fonseca, I. M., Santos, M. C. (2002). SACI-2 Attitude Control Subsystem. INPE, 3, 197–209. Available at: http://www2.dem.inpe.br/ijar/SACI_2BlockDiagram.pdf
- Reuter, G. S., Thomson, W. T. (1966). Rotational movement of passive spacecraft. Problems of the orientation of satellites. Moscow: Nauka, 336–350.
- Hubert, C., Swanson, D. (2001). Surface Tension Lockup in the IMAGE Nutation Damper – Anomaly and Recovery. Available at: http://image.gsfc.nasa.gov/publication/document/2001_hubert_swanson.pdf
- Alper, J. R. (1965). Analysis of pendulum damper for satellite wobble damping. Journal of Spacecraft and Rockets, 2 (1), 50–54. doi: 10.2514/3.28120
- Cloutier, G. J. (1969). Nutation damper instability on spin-stabilized spacecraft. AIAA Journal, 7 (11), 2110–2115. doi: 10.2514/3.5565
- Janssens, F. L., van der Ha, J. C. (2011). On the stability of spinning satellites. Acta Astronautica, 68 (7-8), 778–789. doi: 10.1016/j.actaastro.2010.08.008
- Likins, P. W. (1966). Effects of energy dissipation on the free body motions of spacecraft. Available at: http://www.aoe.vt.edu/~cdhall/courses/aoe4065/NASADesignSPs/sp8016.pdf
- Pirogov, V. V. (2006). Stabilization of the rotation axis of the body in space autobalancing passive devices. Actual problems of Russian cosmonautics: Proceedings of the XXX Academic Conference on Astronautics. Available at: http://www.ihst.ru/~akm/30t5.pdf
- Filimonikhin, G. B., Pirogov, V. V., Filimonikhina, I. I. (2008). Using passive autobalancing as the angle of nutation dampers rapidly rotating satellites. System design and analysis of aerospace technology: Proceedings. Publishing Dnepropetrovsk National University, VIII, 105–115.
- Filimonikhin, G. B., Pirogov, V. V., Filimonikhina, I. I. (2013). Research of process of the elimination autobalancers of large nutation angles. Eastern-European Journal of enterprise technologies, 6/7(66), 34–38. Available at: http://journals.uran.ua/eejet/article/view/18705
- Filimonikhin, G. B., Filimonikhina, I. I., Pirogov, V. V. (2014). Stability of Steady-State Motion of an Isolated System Consisting of a Rotating Body and Two Pendulums. International Applied Mechanics, 50 (4), 459–469. doi: 10.1007/s10778-014-0651-9
- Filimonikhin, G. B., Pirogov, V. V. (2005). Stabilization of the Rotation Axis of a Solid by Coupled Perfectly Rigid Bodies. International Applied Mechanics, 41 (8), 937–943. doi: 10.1007/s10778-005-0164-7
- Kane, T. R., Likins, P. W., Levinson, D. A. (1983). Spacecraft Dynamics. McGraw-Hill, New York. 436.
- Mirer, S. A., Sarychev, V. A. (1997). Optimal Parameters of a Spin-Stabilized Satellite with a Pendulum-Like Damper. Cosmic Research, 35 (6), 609–615.
- Thompson, J. M. T. (1985). Instabilities and Catastrophes in Science and Engineering. Moscow: Mir, 254.
- Ol’hovskij, I. I. (1970). The course of theoretical mechanics for physicists. Moscow: Nauka, 569.
- Filimonikhin, G. B. (2002). Stabilization of the pendulums position of the axis of rotation of isolated rigid body. Bulletin of University of Kyiv, 7-8, 67–71.
- Filimonikhin, G. B., Pirogov, V. V., Filimonikhina, I. I. (2007). Attitude stabilization of the rotational axis of a carrying body by pendulum dampers. International Applied Mechanics, 43 (10), 1167–1173. doi: 10.1007/s10778-007-0117-4
- Filimonikhina, I. I., Filimonikhin, G. B. (2007). Conditions for balancing a rotating body in an isolated system with automatic balancers. International Applied Mechanics, 43 (11), 1276–1282. doi: 10.1007/s10778-007-0132-5
- Matrosov, V. M., Rumjancev, V. V., Karapetjan, A. V. (Eds.) (2001). Nonlinear mechanics. Moscow: FIZMATLIT, 432.
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