Abstract
We study an optimal control problem for the spatial retargeting of a rotating rigid body with unit tensor of inertia. We find new geometric properties of the extremals in this variational problem in the nondegenerate case. We give a detailed description of the extremal “collapse” effect and its relation to the planar manoeuvre. We also show that each extremal has some rank properties. The results are based on the analysis of the system of equations obtained by applying the formalism of the Pontryagin maximum principle and on the use of first integrals.
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References
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)].
A. N. Sirotin, “The Problem of Power-Consumption-Optimal Retargeting with Simultaneous Retardation of a Spherically Symmetric Body with an Unspecified Time,” Prikl. Mat. Mekh. 68(5), 833–846 (2004) [J. Appl. Math. Mech. (Engl. Transl.) 68 (5), 743–755 (2004)].
A. N. Sirotin, “Time-Optimal Retargeting of a Rotating Spherically Symmetric Body with Stopping Its Motion,” Izv. Akad. Nauk.Mekh. Tverd. Tela, No. 3, 18–27 (1997) [Mech. Solids (Engl. Transl.) 32 (3), 14–21 (1997)].
L. S. Pontryagin, Ordinary Differential Equations (Nauka, Moscow, 1970) [in Russian].
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Original Russian Text © A.N. Sirotin, 2009, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2009, No. 5, pp. 9–17.
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Sirotin, A.N. On some geometric properties of extremals in the optimal retargeting problem for spherically symmetric rigid bodies. Mech. Solids 44, 663–670 (2009). https://doi.org/10.3103/S0025654409050021
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DOI: https://doi.org/10.3103/S0025654409050021