Skip to main content
Log in

A mimmax theory for overdamped systems

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Rayleigh, Lord., Some general theorems relating to vibrations. I. The stationary condition. II. The dissipation function. III. A law of reciprocal character. Proc. London Math. Soc. 4, 357–368 (1873); Scientific Papers 1, 170–184.

    MathSciNet  Google Scholar 

  2. Poincaré, H., Sur les équations aux dérivées partielles de la physique mathématique. Amer. J. Math. 12, 211–294 (1890).

    Article  MathSciNet  Google Scholar 

  3. Fischer, E., Über quadratische Formen mit reellen Koeffizienten. Monatshefte für Math. und Physik 16, 234–249 (1905).

    Article  MathSciNet  Google Scholar 

  4. Weyl, H., Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen. Math. Annalen 71, 441–479 (1912).

    Article  MathSciNet  Google Scholar 

  5. Courant, R., & D. Hilbert, Methods of Mathematical Physics I. New York 1953.

  6. Duffin, R. J., A minimax theory for overdamped networks. J. of Rational Mech. Anal. 4, 221–233 (1955).

    MathSciNet  MATH  Google Scholar 

  7. Duffin, R. J., The Rayleigh-Ritz method for dissipative or gyroscopic systems. Quarterly App. Math. 18, 215–221 (1960).

    Article  MathSciNet  Google Scholar 

  8. Morse, M., Functional analysis and abstract variational theory. Mém. des Sci. Math. XCII (1938).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by W. Noll

The results of this paper form a part of the author's thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Carnegie Institute of Technology. The author is indebted to Professor R. J. Duffin for his helpful advice. This work was supported in part by the Army Research Office (Durham) under DA-AROD-31-124-G 78.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rogers, E.H. A mimmax theory for overdamped systems. Arch. Rational Mech. Anal. 16, 89–96 (1964). https://doi.org/10.1007/BF00281333

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281333

Keywords

Navigation