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IssuesArchive of Issues2016-4pp.371-384

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
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Yu.M. Zabolotnov, "Application of the Integral Manifold Method to the Analysis of the Spatial Motion of a Rigid Body Fixed to a Cable," Mech. Solids. 51 (4), 371-384 (2016)
Year 2016 Volume 51 Number 4 Pages 371-384
DOI 10.3103/S0025654416040014
Title Application of the Integral Manifold Method to the Analysis of the Spatial Motion of a Rigid Body Fixed to a Cable
Author(s) Yu.M. Zabolotnov (Samara National Research University, Moskovskoe sh. 34, Samara, 443086 Russia, yumz@yandex.ru)
Abstract We analyze the spatial motion of a rigid body fixed to a cable about its center of mass when the orbital cable system is unrolling. The analysis is based on the integral manifold method, which permits separating the rigid body motion into the slow and fast components. The motion of the rigid body is studied in the case of slow variations in the cable tension force and under the action of various disturbances. We estimate the influence of the static and dynamic asymmetry of the rigid body on its spatial motion about the cable fixation point. An example of the analysis of the rigid body motion when the orbital cable system is unrolling is given for a special program of variations in the cable tension force. The conditions of applicability of the integral manifold method are analyzed.
Keywords orbit, cable system, rigid body, motion about the center of mass, integral manifold method, precession, nutation, asymmetry
References
1.  Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics (Nauka, Moscow, 1973) [in Russian].
2.  A. B. Vasilieva and V. F. Butusov, Asymptotic Expansions of Solutions of Singularly Perturbed Equations (Nauka, Moscow, 1973) [in Russian].
3.  V. V. Strygin and V. A. Sobolev, Separation of Motions by the Method of Integral Manifolds (Nauka, Moscow, 1988) [in Russian].
4.  Yu. M. Zabolotnov, "A Method for Analyzing the Resonance Motion of a Nonlinear Oscillatory System," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 33-45 (1999) [Mech. Solids (Engl. Transl.) 34 (1), 27-37 (1999)].
5.  Yu. M. Zabolotnov and V. V. Lyubimov, "Application of the Method of Integral Manifolds for Construction of Resonant Curves for the Problem of Spacecraft Entry into the Atmosphere," Kosmich. Issled. 41 (5), 481-487 (2003) [Cosmic Res. (Engl. Transl.) 41 (5), 453-459 (2003)].
6.  V. A. Yaroshevskii, Motion of an Uncontrolled Body in the Atmosphere (Mashinostroenie, Moscow, 1978) [in Russian].
7.  V. M. Belokonov, I. V. Belokonov, and Yu. M. Zabolotnov, "Method for Accelerated Modeling of Quasiperiodic Motion of an Almost Axisymmetric Body in the Atmosphere," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 43-50 (1984) [Mech. Solids (Engl. Transl.)].
8.  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)].
9.  V. V. Beletskii and E. M. Levin, Dynamics of Space Tether Systems (Nauka, Moscow, 1990) [in Russian].
10.  M. Kruiff, Tethers in Space (Delta-Utec Space Research, Netherlands, 2011).
11.  S. A. Ishkov and E. M. Levin, "Control of the Orbital Cable System Unrolling," Vestnik Samarsk. Gos. Univ., No. 1, 81-90 (2006).
12.  L. D. Landau and E. M. Lifshits, Theoretical Physics. Vol. 1: Mechanics (Nauka, Moscow, 1988) [in Russian].
13.  Yu. M. Zabolotnov and V. V. Lyubimov, "Non-Linear Resonance Evolution Effects in the Motion of a Rigid Body about a Fixed Point," Prikl. Mat. Mekh. 66 (3), 410-417 (2002) [J. Appl. Math. Mech. (Engl. Transl.) 66 (3), 401-408 (2002)].
14.  V. M. Belokonov and Yu. M. Zabolotnov, "Estimation of the Probability of Resonant Capture of the Spacecraft Reentry Motion," Kosmich. Issled. 40 (5), 503-514 (2002) [Cosmic Res. (Engl. Transl.) 40 (5), 467-478 (2002)].
Received 20 April 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416040014
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