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Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas)

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Abstract

The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem.

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Authors and Affiliations

  1. Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco

    H. Essaouini & L. El Bakkali

  2. Université de Franche-Comté, 2B, Rue des jardins, 25000, Besançon, France

    P. Capodanno

Authors
  1. H. Essaouini
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  2. L. El Bakkali
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  3. P. Capodanno
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Corresponding author

Correspondence to H. Essaouini.

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Essaouini, H., El Bakkali, L. & Capodanno, P. Mathematical study of the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid and a barotropic gas (Oscillations of a pendulum with almost homogeneous liquid and gas). Z. Angew. Math. Phys. 62, 849–868 (2011). https://doi.org/10.1007/s00033-011-0118-3

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  • DOI: https://doi.org/10.1007/s00033-011-0118-3

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