IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1882-d828542.html
   My bibliography  Save this article

Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors

Author

Listed:
  • Víctor Lanchares

    (Department of Mathematics and Computation, Universidad de La Rioja, 26006 Logroño, Spain)

  • Manuel Iñarrea

    (Applied Physics, Universidad de La Rioja, 26006 Logroño, Spain)

  • Ana Isabel Pascual

    (Department of Mathematics and Computation, Universidad de La Rioja, 26006 Logroño, Spain)

  • Antonio Elipe

    (Department of Applied Mathematics, Universidad de Zaragoza, 50009 Zaragoza, Spain)

Abstract

In this paper, we consider the motion of an asymmetric heavy gyrostat, when its center of mass lies along one of the principal axes of inertia. We determine the possible permanent rotations and, by means of the Energy-Casimir method, we give sufficient stability conditions. We prove that there exist permanent stable rotations when the gyrostat is oriented in any direction of the space, by the action of two spinning rotors, one of them aligned along the principal axis, where the center of mass lies. We also derive necessary stability conditions that, in some cases, are the same as the sufficient ones.

Suggested Citation

  • Víctor Lanchares & Manuel Iñarrea & Ana Isabel Pascual & Antonio Elipe, 2022. "Stability Conditions for Permanent Rotations of a Heavy Gyrostat with Two Constant Rotors," Mathematics, MDPI, vol. 10(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1882-:d:828542
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1882/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1882/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Iñarrea, M. & Lanchares, V. & Pascual, A.I. & Elipe, A., 2017. "Stability of the permanent rotations of an asymmetric gyrostat in a uniform Newtonian field," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 404-415.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aslanov, Vladimir S. & Sizov, Dmitry A., 2022. "Chaotic pitch motion of an aerodynamically stabilized magnetic satellite in polar orbits," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Dmitry Roldugin & Mikhail Ovchinnikov, 2023. "Terminal One Axis Stabilization Properties of a Spinning Satellite Employing Simple Magnetic Attitude Control," Mathematics, MDPI, vol. 11(6), pages 1-14, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:gam:jmathe:v:10:y:2022:i:11:p:1882-:d:828542. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.