IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip1s0960077925006563.html
   My bibliography  Save this article

Energy function of 2D and 3D coarse systems

Author

Listed:
  • Ginoux, Jean-Marc
  • Meucci, Riccardo
  • Llibre, Jaume
  • Sprott, Julien Clinton

Abstract

In this work, while using the Flow Curvature Method developed by one of us (JMG), we prove that the energy function of two and three-dimensional coarse systems involving a small parameter μ can be directly deduced from the curvature of their trajectory curves when μ tends to zero. Such a result thus confirms the relationship between curvature and energy function for a certain class of differential systems already established in one of our previous contributions. Then, we state that the rate of change of the energy function of such coarse systems is equal to the scalar product of the velocity vector field and its first time derivative, i.e. the acceleration vector field. The comparison of these results with the so-called Frénet frame enables to prove that energy function is proportional to the normal component of the acceleration when μ tends to zero while the rate of change of the energy function is proportional to the tangential component of the acceleration at first order in μ. Two and three-dimensional examples are then used to emphasize these two main results.

Suggested Citation

  • Ginoux, Jean-Marc & Meucci, Riccardo & Llibre, Jaume & Sprott, Julien Clinton, 2025. "Energy function of 2D and 3D coarse systems," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
  • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006563
    DOI: 10.1016/j.chaos.2025.116643
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925006563
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2025.116643?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.