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Method for Defining Principal Modes of Nonlinear Systems Utilizing Infinite Determinants

In: Selected Papers of Demetrios G. Magiros

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  • Demetrios G. Magiros

    (General Electric Company, Missile and Space Vehicle Department)

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.

Suggested Citation

  • Demetrios G. Magiros, 1985. "Method for Defining Principal Modes of Nonlinear Systems Utilizing Infinite Determinants," Springer Books, in: S. G. Tzafestas (ed.), Selected Papers of Demetrios G. Magiros, chapter 20, pages 272-278, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-5368-0_20
    DOI: 10.1007/978-94-009-5368-0_20
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