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Oscillations lentement forcées du pendule simple

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Summary

We consider the pendulum equation

$$\ddot x + \sin x = \bar b\left( {x = x\left( \tau \right)} \right)$$

where the momentum¯b is slowly and periodically varying, of the form¯b=b cos(ɛτ),ɛ small. Using non-standard analysis techniques, we study oscillatory or non-oscillatory phases of the solutions, as well as their amplitude. Thus one gets arguments to prove the existence of different kinds of periodic solutions, some of them being of oscillatory type all the time, others having (sometimes very) big amplitude.

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Authors and Affiliations

  1. Université de Sidi Bel Abbes, Algérie

    N. Sari

  2. Dépt de Mathématiques, Ile de Saulcy, F57045, Metz-Cedex, France

    B. V. Schmitt

Authors
  1. N. Sari
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  2. B. V. Schmitt
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Sari, N., Schmitt, B.V. Oscillations lentement forcées du pendule simple. Z. angew. Math. Phys. 41, 480–500 (1990). https://doi.org/10.1007/BF00945952

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  • DOI: https://doi.org/10.1007/BF00945952

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