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

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  • 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
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    References listed on IDEAS

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    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.
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    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. 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.
    3. 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.
    4. Velasco-Juan, M. & Fujioka, J., 2022. "Lagrangian nonlocal nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. 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).
    6. 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.

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