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Method for Defining Principal Modes of Nonlinear Systems Utilizing Infinite Determinants

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Selected Papers of Demetrios G. Magiros

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Abstract

A method for calculation of “principal modes” of linear or nonlinear systems is discussed. The physical definition of “principal modes” is formulated mathematically in two ways. The trial solution of the differential equation of the motion of the system is taken in an appropriate structure. The calculation of principal modes leads to infinite determinants of Hill’s and von Koch’s type, which are analyzed. The above method yields the possibility of getting the “principal modes” in the form of a series, all the coefficients of which can be calculated.

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References

  1. (a) D. G. Magiros, Proc. Natl. Acad. Sci. U. S., Dec. (1960). (b) D. G. Magiros, Proc. Natl. Acad. Sci. U. S., June (1961).

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  2. W. Magnus, “Infinite determinants in the theory of Mathieu’s and Hill’s equations,” Research Report No. BR-1, Mathematical Research Group, Washington Square College of Arts and Science, New York University, 1953.

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  3. H. von Koch, Compt. rend., 120, 144 (1895).

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  4. L. Brillouin, Wave Propagation in Periodic Structures (Dover Publications, New York, 1953), 2nd ed., pp. 34, 35.

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  5. H. Wall, Analytic Theory of Continued Fractions (D. Van Nostrand Company, Inc., Princeton, New Jersey, 1948), pp. 26, 42, and 51.

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Author information

Authors and Affiliations

  1. Missile and Space Vehicle Department, General Electric Company, Philadelphia, Pennsylvania, USA

    Demetrios G. Magiros

Authors
  1. Demetrios G. Magiros
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Editor information

Editors and Affiliations

  1. Electrical Engineering Department, National Technical University, Athens, Greece

    S. G. Tzafestas

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© 1985 D. Reidel Publishing Company, Dordrecht, Holland

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Magiros, D.G. (1985). Method for Defining Principal Modes of Nonlinear Systems Utilizing Infinite Determinants. In: Tzafestas, S.G. (eds) Selected Papers of Demetrios G. Magiros. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5368-0_20

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  • DOI: https://doi.org/10.1007/978-94-009-5368-0_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8869-5

  • Online ISBN: 978-94-009-5368-0

  • eBook Packages: Springer Book Archive

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