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Print ISSN 0025-6544
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A.N. Sirotin, "Flat Turn as an Admissible Extremal in the Optimal Rotation Control Problem for an Asymmetric Body," Mech. Solids. 47 (1), 1-18 (2012)
Year 2012 Volume 47 Number 1 Pages 1-18
DOI 10.3103/S0025654412010013
Title Flat Turn as an Admissible Extremal in the Optimal Rotation Control Problem for an Asymmetric Body
Author(s) A.N. Sirotin (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, asirotin2@yandex.ru)
Abstract The problem of optimal control of rotation of an asymmetric rigid body is studied. An integrally quadratic functional characterizing the total energy costs is taken as the criterion. It is shown that, under certain conditions, the problem has a nontrivial extremal corresponding to a 180-degree flat turn, i.e., rotation about an axis fixed in the inertial space. The obtained results are based on an analysis of the equations arising after the application of the Pontryagin maximum principle (PMP) formalism.
Keywords optimal control, rotation, asymmetric rigid body, maximum principle
References
1.  A. N. Sirotin, "Analytical Solutions in the Problem of the Optimal Control of the Rotation of an Axisymmetric Body," Prikl. Mat. Mekh. 70 (2), 225-235 (2006) [J. Appl. Math. Mech. (Engl. Transl.) 70 (2), 199-209 (2006)].
2.  K. B. Alekseev, Extensive Control of Space Craft Attitude (Mashinostroenie, Moscow, 1977) [in Russian].
3.  A. N. Sirotin, "The Existence of Smooth Solutions in a Problem of the Optimal Control of the Rotation of an Axisymmetric Rigid Body," Prikl. Mat. Mekh. 72 (3), 399-409 (2008) [J. Appl. Math. Mech. (Engl. Transl.) 72 (3), 270-278 (2008)].
4.  E. Kamke, Handbook on Ordinary Differential Equations (Fizmatgiz, Moscow, 1961).
5.  A. I. Lurie, Analytic Mechanics (Fizmatgiz, Moscow, 1961; Springer, Berlin, 2001).
6.  L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1965; Pergamon Press, Oxford, 1976).
Received 16 June 2009
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