IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i5p2645-2652.html
   My bibliography  Save this article

General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems

Author

Listed:
  • Musielak, Z.E.

Abstract

Equations of motion describing dissipative dynamical systems with coefficients varying either in time or in space are considered. To identify the equations that admit a Lagrangian description, two classes of non-standard Lagrangians are introduced and general conditions required for the existence of these Lagrangians are determined. The conditions are used to obtain some non-standard Lagrangians and derive equations of motion resulting from these Lagrangians.

Suggested Citation

  • Musielak, Z.E., 2009. "General conditions for the existence of non-standard Lagrangians for dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2645-2652.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2645-2652
    DOI: 10.1016/j.chaos.2009.03.171
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003282
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.171?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.

    References listed on IDEAS

    as
    1. El Naschie, M.S., 2007. "On gauge invariance, dissipative quantum mechanics and self-adjoint sets," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 271-273.
    2. Musielak, Z.E. & Roy, D. & Swift, L.D., 2008. "Method to derive Lagrangian and Hamiltonian for a nonlinear dynamical system with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 894-902.
    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. Diana T. Pham & Zdzislaw E. Musielak, 2023. "Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and Their Role in Population Dynamics," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    2. El-Nabulsi, Rami Ahmad & Khalili Golmankhaneh, Alireza & Agarwal, Praveen, 2022. "On a new generalized local fractal derivative operator," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Zdzislaw E. Musielak & Niyousha Davachi & Marialis Rosario-Franco, 2020. "Special Functions of Mathematical Physics: A Unified Lagrangian Formalism," Mathematics, MDPI, vol. 8(3), pages 1-17, March.
    4. Song, Chuan-Jing & Zhang, Yi, 2017. "Conserved quantities for Hamiltonian systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 24-36.
    5. Rami Ahmad El-Nabulsi, 2015. "From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity," Mathematics, MDPI, vol. 3(3), pages 1-19, August.
    6. Velasco-Juan, M. & Fujioka, J., 2022. "Lagrangian nonlocal nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

    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.
    1. Shams, M. & Vaezpour, S.M., 2009. "Best approximation on probabilistic normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1661-1667.
    2. El Naschie, M.S., 2007. "SU(5) grand unification in a transfinite form," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 370-374.
    3. Wu, Guo-cheng, 2009. "Prolongation approach to Lax pairs and Bäcklund transformation of the variable coefficient KdV equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 408-411.
    4. Alimohammady, Mohsen & Esmaeli, Abdolreza & Saadati, Reza, 2009. "Completeness results in probabilistic metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 765-769.
    5. Giné, Jaume, 2008. "On the origin of the deflection of light," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 1-6.
    6. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.

    More about this item

    Statistics

    Access and download statistics

    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:42:y:2009:i:5:p:2645-2652. 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: 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.