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Volume 14, Issue 2 (2022), Pages [121] - [179]

ON THE EQUILIBRIA AND BIFURCATIONS OF A ROTATING DOUBLE PENDULUM

[1] Soumyabrata Maiti, Jyotirmoy Roy, Asok K. Mallik and Jayanta K. Bhattacharjee, Nonlinear dynamics of a rotating double pendulum, Physics Letters A 380(3) (2016), 408-412.

 

DOI: https://doi.org/10.1016/j.physleta.2015.11.003

 

[2] Robert H. Lewis, Dixon-EDF: The Premier Method for Solution of Parametric Polynomial Systems, In Applications of Computer Algebra Vol. 198, Edited by Ilias S. Kotsireas and Edgar Martinez-Moro (Springer International Publishing) p. 237-256, series Title: Proceedings in Mathematics & Statistics (2017).

 

DOI: https://doi.org/10.1007/978-3-319-56932-1_16

 

[3] A.-L. Dixon, The eliminant of three quantics in two independent variables: Second Paper, Proceedings of the London Mathematical Society 7(1) (1909), 473-492.

 

DOI: https://doi.org/10.1112/plms/s2-7.1.473

 

[4] Fermat, A Computer Algebra System, Robert H. Lewis (2017).

 

http://home.bway.net/lewis/

 

[5] The Double Pendulum, In: Chaos: A Program Collection for the PC, Springer, Berlin, Heidelberg, 2008.

 

DOI: https://doi.org/10.1007/978-3-540-74867-0_5

 

[6] S. Samaranayake and A. K. Bajaj, Bifurcations in the dynamics of an orthogonal double pendulum, Nonlinear Dynamics 4(6) (1993), 605-603.

 

DOI: https://doi.org/10.1007/BF00162234

 

[7] P. Yu and Q. Bi, Analysis of non-linear dynamics and bifurcations of a double pendulum, Journal of Sound and Vibration 217(4) (1998), 691-736.

 

DOI: https://doi.org/10.1006/jsvi.1998.1781

 

[8] Bi Qinsheng and Chen Yushu, Bifurcation analysis of a double pendulum with internal resonance, Applied Mathematics and Mechanics 21(3) (2000), 255-264.

 

DOI: https://doi.org/10.1007/BF02459003

 

[9] R. H. Avanço, J. M. Balthazar, A. M. Tusset and M. A. Ribeiro, Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone, Zeitschrift für Angewandte Mathematik und Mechanik 101(12) (2021), e202000197.

 

DOI: https://doi.org/10.1002/zamm.202000197

 

[10] Thomas J. Bridges and Kyriakos V. Georgiou, A transverse spinning double pendulum, Chaos, Solitons & Fractals 12(1) (2001), 131-144.

 

DOI: https://doi.org/10.1016/S0960-0779(99)00180-0

 

[11] Double Pendulum by stevenbtroy.

 

https://www.youtube.com/watch?v=U39RMUzCjiU

 

[12] Iron Man, film produced by Marvel Studios, Burbank, CA (distributed by Paramount Pictures, 5555 Melrose Ave., Hollywood, CA 90038; released 2008).

 

[13] Swinging Sticks.

 

https://www.the-swinging-sticks.com