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Resonant oscillations driven by a nonlinear forcing term

Резонансные осцилляции, обусловленные нелинейным членом

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The resonant oscillations of a linear system, driven by a nonlinear forcing term of quite a general type, are here treated mainly by the Hamiltonian formalism, starting from the Krylov-Bogoliubov approximate solutions. From the review of many practical examples, this work evolves till the attainment of complete and general solutions, through a proper framing of these examples in the Hamilton formalism. Beyond several original calculations, some ultimate demonstrations, regarding a few particular cases of separatrix curves, are performed.

Riassunto

Le oscillazioni risonanti di un sistema lineare, forzato da un termine non lineare, sono trattate principalmente con il formalismo hamiltoniano, partendo dalle soluzioni approssimate secondo Krylov-Bogoliubov. Il lavoro evolve da una rassegna di parecchi esempi concreti fino al conseguimento di soluzioni complete e generali, tramite un opportuno inquadramento di questi esempi nel formalismo di Hamilton. Oltre a numerosi calcoli originali, si eseguono delle dimostrazioni definitive, riguardanti alcuni casi particolari di curve separatrici.

Резюме

Резонансные осцилляции линейной системы, обусловленные нелинейным членом общего вида, рассматриваются в рамках Гамильтонова формализма, исходя из приближенных решений Крылова-Боголюбова. Из анализа большого количества практических примеров получаются полные и общие решения в рамках Гамильтонова формализма. Помимо численных вычислений, проводится подробное рассмотрение нескольких специальных случаев раздеяьющихся кривых.

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Author notes

  1. G. Dellavalle

    Present address: ELSAG (Elettronica San Giorgio), Genova, Italia

  2. G. Rizzitelli

    Present address: Facoltà di Architettura dell’Università, Istituto di Discipline Scientifiche e Tecniche, Genova, Italia

Authors and Affiliations

  1. Istituto di Scienze Fisiche dell’Università, Genova, Italia

    M. Conte, G. Dellavalle & G. Rizzitelli

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italia

    M. Conte, G. Dellavalle & G. Rizzitelli

Authors
  1. M. Conte
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  2. G. Dellavalle
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  3. G. Rizzitelli
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Conte, M., Dellavalle, G. & Rizzitelli, G. Resonant oscillations driven by a nonlinear forcing term. Nuov Cim B 57, 59–81 (1980). https://doi.org/10.1007/BF02722402

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