Conformable Lagrangian Mechanics of Actuated Pendulum
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...
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2025-05-01
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| author | Adina Veronica Crişan Cresus Fonseca de Lima Godinho Claudio Maia Porto Ion Vasile Vancea |
| author_facet | Adina Veronica Crişan Cresus Fonseca de Lima Godinho Claudio Maia Porto Ion Vasile Vancea |
| author_sort | Adina Veronica Crişan |
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| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. This dependence can describe internal variations such as viscous friction, transmission, or environmental effects. We solve the equations of motion analytically for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> and using Frobenius’ method for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≠</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>. |
| format | Article |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
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| spelling | doaj-art-8135f6368327433683e14a6dee40abdb2025-08-20T03:47:57ZengMDPI AGMathematics2227-73902025-05-011310163410.3390/math13101634Conformable Lagrangian Mechanics of Actuated PendulumAdina Veronica Crişan0Cresus Fonseca de Lima Godinho1Claudio Maia Porto2Ion Vasile Vancea3Department of Mechanical Systems Engineering, Technical University of Cluj-Napoca, 103–105 Muncii Bld., 400641 Cluj-Napoca, RomaniaDepartment of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, BrazilDepartment of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, BrazilDepartment of Physics, Federal Rural University of Rio de Janeiro, Cx. Postal 23851, BR 465 Km 7, Seropédica 23890-000, RJ, BrazilIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>. This dependence can describe internal variations such as viscous friction, transmission, or environmental effects. We solve the equations of motion analytically for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula> and using Frobenius’ method for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>≠</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/13/10/1634conformable calculusconformable mechanicsfractal mechanicsconformable actuated pendulum |
| spellingShingle | Adina Veronica Crişan Cresus Fonseca de Lima Godinho Claudio Maia Porto Ion Vasile Vancea Conformable Lagrangian Mechanics of Actuated Pendulum Mathematics conformable calculus conformable mechanics fractal mechanics conformable actuated pendulum |
| title | Conformable Lagrangian Mechanics of Actuated Pendulum |
| title_full | Conformable Lagrangian Mechanics of Actuated Pendulum |
| title_fullStr | Conformable Lagrangian Mechanics of Actuated Pendulum |
| title_full_unstemmed | Conformable Lagrangian Mechanics of Actuated Pendulum |
| title_short | Conformable Lagrangian Mechanics of Actuated Pendulum |
| title_sort | conformable lagrangian mechanics of actuated pendulum |
| topic | conformable calculus conformable mechanics fractal mechanics conformable actuated pendulum |
| url | https://www.mdpi.com/2227-7390/13/10/1634 |
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