Novel Approximations to the (Un)forced Pendulum–Cart System: Ansatz and KBM Methods

Weaam Alhejaili, Alvaro H. Salas and Samir A. El-Tantawy ()
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Weaam Alhejaili: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Alvaro H. Salas: FIZMAKO Research Group, Department of Mathematics and Statistics, Universidad Nacional de Colombia, Manizales 500001, Colombia
Samir A. El-Tantawy: Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt

Mathematics, 2022, vol. 10, issue 16, 1-12

Abstract: In the present investigation, some novel analytical approximations to both unforced and forced pendulum–cart system oscillators are obtained. In our investigation, two accurate and effective approaches, namely, the ansatz method with equilibrium point and the Krylov–Bogoliubov–Mitropolsky (KBM) method, are implemented for analyzing pendulum–cart problems.The obtained results are compared with the Runge–Kutta (RK4) numerical approximation. The obtained approximations using both ansatz and KBM methods show good coincidence with RK4 numerical approximation. In addition, the global maximum error is estimated as compared to RK4 numerical approximation.

Keywords: pendulum–cart system oscillator; analytical approximations; ansatz method; KBM method; Runge–Kutta numerical approach; global maximum error (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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