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

Author

Listed:
  • 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
    Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Al-Baha 1988, Saudi Arabia)

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.

Suggested Citation

  • Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Novel Approximations to the (Un)forced Pendulum–Cart System: Ansatz and KBM Methods," Mathematics, MDPI, vol. 10(16), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2908-:d:887128
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    References listed on IDEAS

    as
    1. Noufe H. Aljahdaly & S. A. El-Tantawy, 2021. "On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics," Mathematics, MDPI, vol. 9(4), pages 1-12, February.
    2. Haifa A. Alyousef & Alvaro H. Salas & Sadah A. Alkhateeb & S. A. El-Tantawy & Fairouz Tchier, 2022. "Some Novel Analytical Approximations to the (Un)damped Duffing–Mathieu Oscillators," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, May.
    3. Alvaro H. Salas & Wedad Albalawi & M. R. Alharthi & S. A. El-Tantawy & Akif Akgul, 2022. "Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations," Complexity, Hindawi, vol. 2022, pages 1-14, May.
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    Citations

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    Cited by:

    1. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2022. "Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators," Mathematics, MDPI, vol. 10(23), pages 1-13, November.
    2. Weaam Alhejaili & Alvaro H. Salas & Samir A. El-Tantawy, 2023. "Ansatz and Averaging Methods for Modeling the (Un)Conserved Complex Duffing Oscillators," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    3. Alvaro H. Salas & Ma’mon Abu Hammad & Badriah M. Alotaibi & Lamiaa S. El-Sherif & Samir A. El-Tantawy, 2022. "Closed-Form Solutions to a Forced Damped Rotational Pendulum Oscillator," Mathematics, MDPI, vol. 10(21), pages 1-13, October.

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