Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders

Vasile Marinca and Nicolae Herisanu
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Vasile Marinca: Center for Fundamental Technical Research, Romanian Academy, 300222 Timisoara, Romania
Nicolae Herisanu: Center for Fundamental Technical Research, Romanian Academy, 300222 Timisoara, Romania

Mathematics, 2020, vol. 8, issue 8, 1-18

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.

Keywords: simple pendulum; optimal auxiliary functions method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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