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Introduction

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Book cover Lagrangian Optics

Abstract

Variational principles are of great universality and play a major role in the description of natural phenomena. The minimum hypothesis to explain nature has been present in ideas presented by early Greeks whose philosophy seems to be based on the principle that “Nature does nothing in vain”. Such ‘economy’ postulates in the hands of later scientists acted as the foundation for the development of minimum principles such as Fermat’s principle. If one studies the chronological development in the evolution of minimum principles one can get a profound insight into the continuos transformation of a metaphysical canon into an exact natural law.

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References

  1. D.S. Lemons, Perfect form, Princeton University Press, Princeton, N J (1997)

    Google Scholar 

  2. W. Yourgrau and S. Madelstam, Variational principles in Dynamics and Quantum theory Dover, NY, (1968)

    Google Scholar 

  3. C. Lanczos, The variational principles in Mechanics, Dover, NY, (1970)

    Google Scholar 

  4. E. Mach, The science of mechanics, Open court: La Salle, Illinois, (1960). Page 30

    Google Scholar 

  5. R.K. Luneburg, Mathematical theory of optics, Univ. of California press, Berkeley, CA. (1964) page 87.

    Google Scholar 

  6. C. Caratheodory, Geometrische optik, Springer Verlag, Berlin, 1937. page 10.

    Book  MATH  Google Scholar 

  7. V. Ronchi, The nature of light, Harvard University Press, Cambridge, MA (1970)

    Google Scholar 

  8. E.T. Whittaker, A history of the theories of Aether and Electricity, Thomas Nelson and Sons, London Vol. 1 (1951); Vol.2(1953)

    MATH  Google Scholar 

  9. E.T. Bell, Men of Mathematics, Simon and Schuster, NY, 1937

    MATH  Google Scholar 

  10. W.R. Hamilton, The mathematical papers of Sir William Rowan Hamilton, ed. A.W. Conway and J.L. Synge, Vol. 1: Geometrical optics, Cambridge Univ. Press, London (1931); Vol.2: Dynamics, Cambridge Univ. Press, London, 1940

    Google Scholar 

  11. H. Goldstein, Classical Mechanics, Addison Wesley, Cambridge, Mass., (1956)

    Google Scholar 

  12. H. Bruns, Abh. Kgl. Sachs. Ges.Wiss., Math-phys. KL, 21,323 (1985); see also J.L Synge, J. Opt. Soc. Am., 27:138, (1937)

    Google Scholar 

  13. J. Evans and M. Rosenquist, ‘F=ma optics’, Am. J. Phys. 54:876–883 (1986)

    Article  ADS  Google Scholar 

  14. D. Gloge, D. Marcuse, Formal quantum theory of light rays, J. Opt Soc. Am., 59:1629, (1969)

    Article  ADS  Google Scholar 

  15. H. Busch, Zeitschr. Physik, 81,:974 (1926)

    Google Scholar 

  16. H.A. Buchadahl, An introduction to Hamiltonian optics, Dover, NY, (1993)

    Google Scholar 

  17. Y.S. Kim and M.S. Noz, Phase space picture of Quantum mechanics, world scientific, Singapore (1991)

    Google Scholar 

  18. C. Lejeure and J. Aubert, in Applied charged particle optics, ed. A. Septier, Adv. in Electron, and electr. Physics suppl. 13A, Academic press, NY 1980.

    Google Scholar 

  19. A. Torre, A unified point of view to radiation and changed beam transport, I1 Nuovo Cimento, 112:409 (1999)

    Article  Google Scholar 

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© 2002 Springer Science+Business Media New York

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Lakshminarayanan, V., Ghatak, A.K., Thyagarajan, K. (2002). Introduction. In: Lagrangian Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1711-5_1

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  • DOI: https://doi.org/10.1007/978-1-4615-1711-5_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7582-1

  • Online ISBN: 978-1-4615-1711-5

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