Skip to main content
SpringerLink
Log in

The Condition of Hydrostatic Equilibrium of Stellar Models Using Optimal Control

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The condition of hydrostatic equilibrium of relativistic stellar models is formulated as an optimal control problem. Application of Pontryagin's maximum principle leads directly to the Tolman-Oppenheimer-Volkoff equation.

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

  • Athans, M. and Falb, P.L.: 1966, Optimal Control, McGraw-Hill, New York.

    Google Scholar 

  • Craven, B.D.: 1995, Control and Optimization, Chapman & Hall, London.

    Google Scholar 

  • Feldbaum, A.A.: 1965, Optimal Control Systems, Academic Press, New York.

    Google Scholar 

  • Harrison, B.K., Thorne, K.S., Wakano, M. and Wheeler, J.A.: 1965, Gravitation Theory and Gravitational Collapse, University of Chicago press, Chicago, pp. 16‐18.

    Google Scholar 

  • Lee, E.B. and Markus, L.: 1967, Foundations of Optimal Control Theory, John Wiley, New York.

    Google Scholar 

  • Miliutin, A.A. and Osmolovskii, N.P: 1998, Calculus of Variations and Optimal Control, American Mathematical Society, Providence.

    Google Scholar 

  • Misner, C.W., Thorne, K.S. and Wheeler, J.A.: 1973, Gravitation, Freeman, San Francisco, Part V.

    Google Scholar 

  • Oppenheimer, J.R. and Volkoff, G.: 1939, Phys. Rev. 55, 374.

    Article  MATH  ADS  Google Scholar 

  • Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. and Mishchenko, E.F.: 1962, The Mathematical Theory of Control Processes, Interscience, New York.

    Google Scholar 

  • Tolman, R.C.: 1934, Relativity, Thermodynamics and Cosmology, Clarendon Press, Oxford, pp. 242‐243.

    Google Scholar 

  • Weinberg, S.: 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley, New York, pp. 306‐307.

    Google Scholar 

  • Zadeh, L.A. and Desoer, C.A.: 1963, Linear System Theory: The State Space Approach, McGraw-Hill, New York.

    Google Scholar 

Download references

Author information

Author notes

  1. Salah Haggag

    Present address: Mathematics Department, Faculty of Science, Al-Azhar University at Assiut, Assiut, 71524, Egypt

Authors and Affiliations

  1. Department of Physics and Astronomy, University of South Carolina, Columbia, South Carolina, 29208, USA

    Salah Haggag & John L. Safko

Authors
  1. Salah Haggag
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Safko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haggag, S., Safko, J.L. The Condition of Hydrostatic Equilibrium of Stellar Models Using Optimal Control. Astrophysics and Space Science 283, 369–373 (2003). https://doi.org/10.1023/A:1021684407650

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1021684407650

Keywords

Search

Navigation