Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2017-3pp.278-288

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 52, Issue 3 / 2017 | Next article >>
Yu.M. Zabolotnov and A.A. Lobanov, "Synthesis of a Controller for Stabilizing the Motion of a Rigid Body about a Fixed Point," Mech. Solids. 52 (3), 278-288 (2017)
Year 2017 Volume 52 Number 3 Pages 278-288
DOI 10.3103/S0025654417030050
Title Synthesis of a Controller for Stabilizing the Motion of a Rigid Body about a Fixed Point
Author(s) Yu.M. Zabolotnov (S.P. Korolev Samara National Research University, Moskovskoe sh. 34, Samara, 443086 Russia, yumz@yandex.ru)
A.A. Lobanov (S.P. Korolev Samara National Research University, Moskovskoe sh. 34, Samara, 443086 Russia)
Abstract A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averaging method. The latter is used to solve the Hamilton-Jacobi-Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).
Keywords rigid body, motion about a fixed point, Lagrange top, controller synthesis, dynamic programming, averaging method
References
1.  R. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, 1957; Izdat. Inostr. Lit., Moscow, 1960).
2.  A. M. Letov, Flight Dynamics and Control (Nauka, Moscow, 1969) [in Russian].
3.  R. E. Kalman, P. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory (McGraw Hill, 1969; Editorial URSS, Moscow, 2004).
4.  V. N. Lebedev, Computation of Motion of a Spacecraft with Small Traction (VTs AN SSSR, Moscow, 1967) [in Russian].
5.  F. L. Chernousko, L. D. Akulenko, and B. N. Sokolov, Control of Oscillations (Nauka, Moscow, 1980) [in Russian].
6.  N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics (Nauka, Moscow, 1969) [in Russian].
7.  V. V. Salmin, S. A. Ishkov, and O. L. Starinova, Methods for Solving Variational Problems of Mechanics of Space Flight with Small Traction (Izdat. SNTs RAN, Samara, 2006) [in Russian].
8.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Theory of Vibrations (Nauka, Moscow, 1988) [in Russian].
9.  V. A. Yaroshevskii, Motion of Uncontrolled Body in the Atmosphere (Mashinostroenie, Moscow, 1978) [in Russian].
10.  Yu. M. Zabolotnov, "Asymptotic Analysis of the Quasilinear Equations of Movement in an Atmosphere Spacecraft with Small Asymmetry," Kosmich. Issled. 31 (6), 39-50 (1993) [Cosmic Res. (Engl. Transl.)].
11.  Yu. M. Zabolotnov and O. N. Naumov, "Motion of a Descent Capsule Relative to Its Center of Mass when Deploying the Orbital Tether System," Kosmich. Issled. 50 (2), 183-193 (2012) [Cosmic Res. (Engl. Transl.) 50 (2), 177-187 (2012)].
12.  V. V. Lyubimov, "External Stability of Resonances in the Motion of an Asymmetric Rigid Body with a Strong Magnet in the Geomagnetic Field," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 13-27 (2010) [Mech. Solids (Engl. Transl.) 45 (1), 10-21 (2010)].
13.  A. A. Dmitrievskii, L. N. Lysenko, and S. S. Bogodistov External Ballistics (Mashinostroenie, Moscow, 1991) [in Russian].
14.  Yu. M. Zabolotnov and V. V. Lyubimov, "Secondary Resonance Effects in the Rotation of a Rigid Body about a Fixed Point," Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 49-59 (2002) [Mech. Solids (Engl. Transl.) 37 (1), 39-46 (2002)].
15.  M. M. Khapaev, Averaging in Stability Theory (Nauka, Moscow, 1988) [in Russian].
16.  Yu. M. Zabolotnov, "Asymptotic Analysis of Quasilinear Equations of Motion in the Atmosphere of Spacecraft with Small Asymmetry. III," Kosmich. Issled. 32 (4-5), 112-125 (1994) [Cosmic. Res. (Engl. Transl.)].
17.  V. M. Belokonov and Yu. M. Zabolotnov, "Estimation of the Probability of Capture into a Resonance Mode of Motion for a Spacecraft during Its Descent in the Atmosphere," Kosmich. Issled. 40 (5), 503-514 (2002) [Cosmic Res. (Engl. Transl.) 40 (5), 467-478 (2002)].
Received 29 April 2014
Link to Fulltext
<< Previous article | Volume 52, Issue 3 / 2017 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100