Conformable Lagrangian Mechanics of Actuated Pendulum

Adina Veronica Crişan, Cresus Fonseca de Lima Godinho, Claudio Maia Porto and Ion Vasile Vancea ()
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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

Mathematics, 2025, vol. 13, issue 10, 1-36

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 .

Keywords: conformable calculus; conformable mechanics; fractal mechanics; conformable actuated pendulum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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