Conformable Lagrangian Mechanics of Actuated Pendulum - Adina Veronica Crişan; Cresus Fonseca de Lima Godinho; Claudio Maia Porto; Ion Vasile Vancea (Mathematics)
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 <semantics>α</semantics>. This dependence can describe internal variations such as viscous friction, transmission, or environmental effects. We solve the equations of motion analytically for <semantics>α=1/2</semantics> and using Frobenius’ method for <semantics>α≠1/2</semantics>.