Skip to main content
SpringerLink
Log in

A Family of Extremal Angular Velocity Vector Functions with a Constant Absolute Value in the Problem of Optimal Reorientation of a Spherically Symmetric Body with Minimal Energy Consumption

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The problem of optimal control of reorientation of an absolutely rigid spherically symmetric body is investigated. An integral-quadratic functional characterizing the total energy consumption was chosen as a criterion for the effectiveness of maneuver. Main moment of applied external forces serves as control. In this problem, for the first time, a family of analytic extremal trajectories is obtained, which are uniquely determined in accordance with the requirement that the absolute value of the angular velocity vector function be constant in time. Illustrative examples are provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. A. Agrachev and Yu. L. Sachkov, Geometric Control Theory (Fizmatlit, Moscow, 2005) [in Russian].

    MATH  Google Scholar 

  2. L. S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatlit, Moscow, 1961; Gordon & Breach Sci. Publ., New York, 1986).

    MATH  Google Scholar 

  3. K. B. Alekseev, Extensive Spacecraft Orientation Control (Mashinostroyenie, Moscow, 1977) [in Russian].

    Google Scholar 

  4. A. N. Sirotin, “Flat Turn as an Admissible Extremal in the Optimal Rotation Control Problem for an Asymmetric Body,” Izv. Ros. Akad.NaukMekh. Tv. Tela No. 1, 3–26 (2012) [Mech. Sol. (Engl. Transl.) 47 (1), 1-18 (2012)].

    Google Scholar 

  5. A. N. Sirotin, “A Family of Trigonometric Extremals in the Problem of Reorienting a Spherically Symmetrical Body withMinimum Energy Eonsumption,” Prikl. Mat. Mekh. 77 (2), 283–291 (2013) [J. Appl.Math.Mech. (Engl. Transl.) 77 (2), 205-211 (2013)].

    MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was financially supported by the Russian Foundation for Basic Research (17-01-00538).

Author information

Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993, Russia

    T. I. Sirotin

Authors
  1. T. I. Sirotin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. I. Sirotin.

Additional information

Russian Text © Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 3, pp. 16-29.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sirotin, T.I. A Family of Extremal Angular Velocity Vector Functions with a Constant Absolute Value in the Problem of Optimal Reorientation of a Spherically Symmetric Body with Minimal Energy Consumption. Mech. Solids 54, 502–513 (2019). https://doi.org/10.3103/S0025654419040022

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654419040022

Keywords

Search

Navigation