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Conformable Lagrangian Mechanics of Actuated Pendulum

Author

Listed:
  • Adina Veronica Crişan

    (Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 103–105 Muncii Bld., 400641 Cluj-Napoca, Romania)

  • Cresus Fonseca de Lima Godinho

    (Department of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, Brazil)

  • Claudio Maia Porto

    (Department of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, Brazil)

  • Ion Vasile Vancea

    (Department of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, Brazil)

Abstract

In this paper, we construct the conformable actuated pendulum model in the conformable Lagrangian formalism. We solve the equations of motion in the absence of force and in the case of a specific force resulting from torques, which generalizes a well known mechanical model. Our study shows that the conformable model captures essential information about the physical system encoded in the parameters which depend on the conformability factor α . This dependence can describe internal variations such as viscous friction, transmission, or environmental effects. We solve the equations of motion analytically for α = 1 / 2 and using Frobenius’ method for α ≠ 1 / 2 .

Suggested Citation

  • Adina Veronica Crişan & Cresus Fonseca de Lima Godinho & Claudio Maia Porto & Ion Vasile Vancea, 2025. "Conformable Lagrangian Mechanics of Actuated Pendulum," Mathematics, MDPI, vol. 13(10), pages 1-36, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1634-:d:1657427
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    References listed on IDEAS

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    1. Zhao, Dazhi & Pan, Xueqin & Luo, Maokang, 2018. "A new framework for multivariate general conformable fractional calculus and potential applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 271-280.
    2. Tarasov, Vasily E., 2025. "“Conformable fractional” derivatives and integrals are integer-order operators: Physical and geometrical interpretations, applications to fractal physics," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    3. Mohammed K. A. Kaabar & Francisco Martínez & Inmaculada Martínez & Zailan Siri & Silvestre Paredes & Antonio Di Crescenzo, 2021. "Novel Investigation of Multivariable Conformable Calculus for Modeling Scientific Phenomena," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, November.
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