The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

1 Moatimid GM, Amer TS. Analytical solution for the motion of a pendulum with rolling wheel: stability analysis. Scientific Reports. 2022 Jul 24;12(1):12628. Search in Google Scholar

2 Haider JA, Muhammad N, Nadeem S, Asghar S. Analytical analysis of the fourth-order Boussinesq equation by traveling wave solutions. International Journal of Modern Physics B. 2023 Jul 10;37(17):22350170. Search in Google Scholar

3 Matrosov I, Morozov Y, Pesterev A. Control of the robot-wheel with a pendulum. In2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference)(STAB) 2020 Jun 3 (1-4). IEEE. Search in Google Scholar

4 Haider JA, Zaman FD, Lone SA, Anwar S, Almutlak SA, Elseesy IE. Exact solutions of Euler–Bernoulli beams. Modern Physics Letters B. 2023 Jul 12:2350161. Search in Google Scholar

5 Palazoğlu TK, Miran W. Experimental investigation of the combined translational and rotational movement on an inclined conveyor on radio frequency heating uniformity. Innovative Food Science & Emerging Technologies. 2018 Jun 1;47:16-23. Search in Google Scholar

6 Tanly NN, Fotsa RT, Woafo P. Complex Dynamics of a Mechanical Mechanism Combining Translational and Rotational Motions. Journal of Vibration Engineering & Technologies. 2022 Jul;10(5):1753-64. Search in Google Scholar

7 Raza MY, Haider JA, Ahammad NA, Guedri K, Galal AM. Insightful study of the characterization of the Cobalt oxide nanomaterials and hydrothermal synthesis. International Journal of Modern Physics B. 2023 Apr 30;37(11):2350101. Search in Google Scholar

8 Panayanthatta N, Clementi G, Ouhabaz M, Costanza M, Margueron S, Bartasyte A, Basrour S, Bano E, Montes L, Dehollain C, La Rosa R. A self-powered and battery-free vibrational energy to time converter for wireless vibration monitoring. Sensors. 2021 Nov 11;21(22):7503. Search in Google Scholar

9 Guler U, Sendi MS, Ghovanloo M. A dual-mode passive rectifier for wide-range input power flow. In2017 IEEE 60th International Midwest Symposium on Circuits and Systems (MWSCAS) 2017 Aug 6 (pp. 1376-1379). IEEE. Search in Google Scholar

10 Chen J, Bao B, Liu J, Wu Y, Wang Q. Pendulum Energy Harvesters: A Review. Energies. 2022 Nov 18;15(22):8674. Search in Google Scholar

11 Hunt JB. Dynamic vibration absorbers. 1979. Search in Google Scholar

12 Nadeem S, Haider JA, Akhtar S, Ali S. Numerical simulations of convective heat transfer of a viscous fluid inside a rectangular cavity with heated rotating obstacles. International Journal of Modern Physics B. 2022 Nov 10;36(28):2250200. Search in Google Scholar

13 Serway RA, Beichner RJ. Physics for Scientists and Engineers 5th edn (Forth Worth, TX: Saunders). Search in Google Scholar

14 Beléndez A, Pascual C, Méndez DI, Beléndez T, Neipp C. Exact solution for the nonlinear pendulum. Revista brasileira de ensino de física. 2007;29:645-8. Search in Google Scholar

15 Parwani RR. An approximate expression for the large angle period of a simple pendulum. European journal of physics. 2003 Oct 10;25(1):37. Search in Google Scholar

16 Haider JA, Rahman JU, Zaman FD, Gul S. Travelling wave solutions of the non-linear wave equations. Acta mechanica et automatica. 2023;17(2). Search in Google Scholar

17 Elmandouh AA. On the integrability of the motion of 3D-Swinging Atwood machine and related problems. Physics Letters A. 2016 Mar 6;380(9-10):989-91. Search in Google Scholar

18 Wang F, Bajaj AK, Kamiya K. Nonlinear normal modes and their bifurcations for an inertially coupled nonlinear conservative system. Nonlinear Dynamics. 2005 Nov;42:233-65. Search in Google Scholar

19 El-Sabaa FM, Amer TS, Gad HM, Bek MA. On the motion of a damped rigid body near resonances under the influence of harmonically external force and moments. Results in Physics. 2020 Dec 1;19:103352. Search in Google Scholar

20 Anurag, Mondal B, Shah T, Chakraborty S. Chaos and order in librating quantum planar elastic pendulum. Nonlinear Dynamics. 2021 Feb;103:2841-53. Search in Google Scholar

21 Haider JA, Asghar S, Nadeem S. Travelling wave solutions of the third-order KdV equation using Jacobi elliptic function method. International Journal of Modern Physics B. 2023 May 10;37(12):2350117. Search in Google Scholar

22 Amer TS, Bek MA, Abohamer MK. On the motion of a harmonically excited damped spring pendulum in an elliptic path. Mechanics Research Communications. 2019 Jan 1;95:23-34. Search in Google Scholar

23 Xu X, Wiercigroch M. Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum. Nonlinear Dynamics. 2007 Jan;47:311-20. Search in Google Scholar

24 Sorokin VS. Analysis of motion of inverted pendulum with vibrating suspension axis at low-frequency excitation as an illustration of a new approach for solving equations without explicit small parameter. International Journal of Non-Linear Mechanics. 2014 Jul 1; 63:1-9. Search in Google Scholar

25 Haider JA, Ahammad NA, Khan MN, Guedri K, Galal AM. Insight into the study of natural convection heat transfer mechanisms in a square cavity via finite volume method. International Journal of Modern Physics B. 2023 Feb 10;37(04):2350038. Search in Google Scholar

26 Khan MM. Variational Iteration Method for the Solution of Differential Equation of Motion of the Mathematical Pendulum and Duffing-Harmonic Oscillator. Earthline Journal of Mathematical Sciences. 2019 May 2;2(1):101-9. Search in Google Scholar

27 Amir M, Haider JA, Ahmad S, Ashraf A, Gul S. Approximate solution of painlevé equation i by natural decomposition method and laplace decomposition method. acta mechanica et automatica. 2023;17(3). Search in Google Scholar

28 Ozis T, Yildirim A. Determination of the frequency-amplitude relation for a Duffing-harmonic oscillator by the energy balance method. Computers and Mathematics with Applications. 2007 Oct 1;54(7):1184-7. Search in Google Scholar

29 Amir M, Awais M, Ashraf A, Ali R, Ali Shah SA. Analytical Method for Solving Inviscid Burger Equation. Punjab University Journal of Mathematics. 2023 Dec 3;55(1). Search in Google Scholar

30 Wang SQ, He JH. Variational iteration method for solving integro-differential equations. Physics letters A. 2007 Jul 23;367(3):188-91 Search in Google Scholar

31 Haider JA, Ahmad S. Dynamics of the Rabinowitsch fluid in a reduced form of elliptic duct using finite volume method. International Journal of Modern Physics B. 2022 Dec 10;36(30):2250217. Search in Google Scholar

32 Liu F, Zhang T, He CH, Tian D. Thermal oscillation arising in a heat shock of a porous hierarchy and its application. Facta Universitatis, Series: Mechanical Engineering. 2022 Nov 30;20(3):633-45. Search in Google Scholar

33 Haider JA, Muhammad N. Computation of thermal energy in a rectangular cavity with a heated top wall. International Journal of Modern Physics B. 2022 Nov 20;36(29):2250212. Search in Google Scholar

34 Haider JA, Muhammad N. Computation of thermal energy in a rectangular cavity with a heated top wall. International Journal of Modern Physics B. 2022 Nov 20;36(29):2250212. Search in Google Scholar

35 He JH. Variational iteration method–a kind of non-linear analytical technique: some examples. International journal of non-linear mechanics. 1999 Jul 1;34(4):699-708. Search in Google Scholar

36 Rahman JU, Mannan A, Ghoneim ME, Yassen MF, Haider JA. Insight into the study of some nonlinear evolution problems: Applications based on Variation Iteration Method with Laplace. International Journal of Modern Physics B. 2023 Jan 30;37(03):2350030. Search in Google Scholar

37 He JH, Latifizadeh H. A general numerical algorithm for nonlinear differential equations by the variational iteration method. International Journal of Numerical Methods for Heat & Fluid Flow. 2020 Oct 15;30(11):4797-810. Search in Google Scholar

38 He JH. Variational iteration method–a kind of non-linear analytical technique: some examples. International journal of non-linear mechanics. 1999 Jul 1;34(4):699-708. Search in Google Scholar

39 He JH. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Computer Methods in Applied Mechanics and Engineering. 1998 Dec 1;167(1-2):57-68. Search in Google Scholar

40 He JH. Variational iteration method—some recent results and new interpretations. Journal of computational and applied mathematics. 2007 Oct 1;207(1): 3-17. Search in Google Scholar

41 Elzaki TM. Application of new transform “Elzaki transform” to partial differential equations. Global Journal of pure and applied Mathematics. 2011;7(1):65-70. Search in Google Scholar

42 Anjum N, He JH. Laplace transform: making the variational iteration method easier. Applied Mathematics Letters. 2019 Jun 1;92:134-8 Search in Google Scholar

43 Moatimid GM, Amer TS. Analytical solution for the motion of a pendulum with rolling wheel: stability analysis. Scientific Reports. 2022 Jul 24;12(1):12628. Search in Google Scholar

44 Nayfeh AH. Introduction to perturbation techniques. John Wiley & Sons; 2011 Apr 8. Search in Google Scholar

45 Ghaleb AF, Abou-Dina MS, Moatimid GM, Zekry MH. Analytic approximate solutions of the cubic–quintic Duffing–van der Pol equation with two-external periodic forcing terms: Stability analysis. Mathematics and Computers in Simulation. 2021 Feb 1;180:129-51. Search in Google Scholar

46 Asghar S, Haider JA, Muhammad N. The modified KdV equation for a nonlinear evolution problem with perturbation technique. International Journal of Modern Physics B. 2022 Sep 30;36(24):2250160. Search in Google Scholar

47 He CH, Amer TS, Tian D, Abolila AF, Galal AA. Controlling the kinematics of a spring-pendulum system using an energy harvesting device. Journal of Low Frequency Noise, Vibration and Active Control. 2022 Sep;41(3):1234-57. Search in Google Scholar