Foundations of Physics

, Volume 7, Issue 1–2, pp 129–136 | Cite as

An extension of the Gauss-Hertz principle

  • Richard L. Moore
Article

Abstract

The Gauss-Hertz principle is extended by the use of existence conditions (or constraints) to obtain a hierarchy of differential equations which include all classical equations of continuum mechanics (including electrodynamics) and the harmonic oscillator potential as well.

Keywords

Differential Equation Classical Equation Harmonic Oscillator Existence Condition Oscillator Potential 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Hertz,The Principles of Mechanics (Dover, New York, 1956).Google Scholar
  2. 2.
    W. Yourgrau and S. Mandelstam,Variational Principles in Dynamics and Quantum Theory, 3rd ed. (Pitman, London, 1968).Google Scholar
  3. 3.
    H. Margenau and G. M. Murphy,The Mathematics of Physics and Chemistry (Van Nostrand, New York, 1943).Google Scholar
  4. 4.
    P. Moon and D. E. Spencer,Field Theory Handbook (Springer-Verlag, Berlin, 1961).Google Scholar
  5. 5.
    R. L. Moore, Pressure Patterns in Vortices: the Smoothest Possible is Found by Use of the Vector Laplace Equation, unpublished; also see On the Stable Equilibrium of a Confined Plasma,Bull. Am. Phys. Soc. 19, 62 (1974); Hooke's Law Derived by Minimization Principles,Tr. 20th Conf. Army Mathematicians, ARO Report 75-1 (1975).Google Scholar
  6. 6.
    I. S. Sokolonikoff,Mathematical Theory of Elasticity (McGraw-Hill, New York, 1956).Google Scholar
  7. 7.
    O. Bjøorgum, On Beltrami vector fields and flows, Part I,Univ Bergen, Årbok 1951, Naturv. rekke No. 1, O. Bjøorgum and T. Godal, On Beltrami vector fields and flows, Part II,Årbok 1952, Naturv. rekke No. 13.Google Scholar
  8. 8.
    E. W. Hobson,The Domain of Natural Science (Dover, New York, 1968), p. 26, and others.Google Scholar
  9. 9.
    V. Bjerknes, J. Bjerknes, H. Solberg, and T. Bergeron,Hydrodynamique Physique (Universitaires de France, Paris, 1934).Google Scholar
  10. 10.
    J. A. Brinkman, A Modernization of MacCullagh's Ether Theory, inMechanics of Generalized Continna, E. Kroner, ed. (Springer-Verlag, New York, 1968), pp. 344–346.Google Scholar
  11. 11.
    R. L. Moore,Bull Am. Phys. Soc. 20, 1433 (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • Richard L. Moore
    • 1
  1. 1.U.S. Army Armament CommandRock Island

Personalised recommendations