Lyapunov stability for a generalized Hénon-Heiles system in a rotating reference frame

  1. Iñarrea, M. 1
  2. Lanchares, V. 1
  3. Palacián, J.F. 2
  4. Pascual, A.I. 1
  5. Salas, J.P. 1
  6. Yanguas, P. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

Journal:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2015

Volume: 253

Pages: 159-171

Type: Article

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DOI: 10.1016/J.AMC.2014.12.072 SCOPUS: 2-s2.0-84920659778 WoS: WOS:000349362400015 GOOGLE SCHOLAR

More publications in: Applied Mathematics and Computation

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Abstract

In this paper we focus on a generalized Hénon-Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classical case; it is a stable equilibrium point regardless of the frequency value of the rotating frame.