Skip to main content
SpringerLink
Log in

Optimal method for swinging the swing

  • Control Theory
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We compute the greatest lower bound of multipliers of the generalized Mathieu equations \( \ddot x \)+(1+p(t))x = 0 with continuous π-periodic functions p(·) satisfying some additional constraints.

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. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.Z., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (The Mathematical Theory of Optimal Processes), Moscow: Nauka, 1976.

    Google Scholar 

  2. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach (Theory of Extremal Processes), Moscow: Nauka, 1974.

    Google Scholar 

  3. Fedorenko, R.P., Priblizhennoe reshenie zadach optimal’nogo upravleniya (Approximate Solution of Optimal Control Problems), Moscow: Nauka, 1978.

    MATH  Google Scholar 

  4. Blansh, G., Mathieu Functions, in Spravochnik po spetsial’nym funktsiyam (Reference Book on Special Functions), Moscow, 1979, pp. 532–538.

  5. Yakubovich, V.A. and Starzhinskii, V.M., Lineinye differentsial’nye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya (Linear Differential Equations with Periodic Coefficients and Their Applications), Moscow: Nauka, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, Russia

    Yu. S. Kolesov

Authors
  1. Yu. S. Kolesov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © Yu.S. Kolesov, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 10, pp. 1488–1494.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolesov, Y.S. Optimal method for swinging the swing. Diff Equat 46, 1491–1497 (2010). https://doi.org/10.1134/S0012266110100137

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266110100137

Keywords

Search

Navigation