Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders
Vasile Marinca, Nicolae Herişanu
Abstract
In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange’s equation. Analytical solutions and natural frequency of the system are calculated. Our results obtained through this new procedure are compared with numerical ones and a very good agreement was found, which proves the accuracy of the method. The presented numerical examples show that the proposed approach is simple, easy to implement and very accurate.
Topics & Concepts
PendulumSimple (philosophy)Nonlinear systemWork (physics)Double pendulumMathematicsEquations of motionControl theory (sociology)Lagrange multiplierNumerical analysisApplied mathematicsNatural frequencyMathematical analysisComputer scienceInverted pendulumClassical mechanicsVibrationPhysicsMathematical optimizationEngineeringMechanical engineeringAcousticsQuantum mechanicsPhilosophyControl (management)EpistemologyArtificial intelligenceExperimental and Theoretical Physics StudiesScientific Research and DiscoveriesQuantum chaos and dynamical systems